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Here at Live Science, we love numbers. And on Pi Day — March 14, or 3/14 — we love to celebrate the world’s most famous irrational number, pi, whose first 10 digits are 3.141592653. 

As the ratio of a circle’s circumference to its diameter, pi is not just irrational, meaning it can’t be written as a simple fraction. It is also transcendental, meaning it’s not the root, or solution, to any polynomial equation, such as x+2X^2+3 = 0.

Pi may be one of the best-known numbers, but for people who are paid to think about numbers all day long, the circle constant can be a bit of a bore. We asked several mathematicians to tell us their favorite non-pi numbers. Here are some of their answers.Tau

People often eat pie on pi day. (Image credit: Shutterstock)

You know what’s cooler than one pie? … Two pies. In other words, two times pi, or the number “tau,” which is roughly 6.28.

“Using tau makes every formula clearer and more logical than using pi,” said John Baez (opens in new tab) , a mathematician at the University of California, Riverside. “Our focus on pi rather than 2pi is a historical accident.”

Tau is what shows up in the most important formulas, he said.

While pi relates a circle’s circumference to its diameter, tau relates a circle’s circumference to its radius — and many mathematicians argue that this relationship is much more important. Tau also makes seemingly unrelated equations nicely symmetrical, such as the one for a circle’s area and an equation describing kinetic and elastic energy.

But tau will not be forgotten on Pi Day! As per tradition, the Massachusetts Institute of Technology will send out decisions at 6:28 p.m. today. A few months from now, on June 28, it will be Tau Day.Natural log base

The natural log is expressed as the symbol “e.” (Image credit: Shutterstock)

The base of natural logarithms — written as “e” for its namesake, the 18th-century Swiss mathematician Leonhard Euler — may not be as famous as pi, but it also has its own holiday. So, while 3.14 is celebrated on March 14, natural log base — the irrational number beginning with 2.718 — is lionized on Feb. 7.

The base of natural logarithms is most often used in equations (opens in new tab) involving logarithms, exponential growth and complex numbers.

“[It] has the wonderful definition as being the one number for which the exponential function y = e^x has a slope equal to its value at every point,” Keith Devlin (opens in new tab) , emeritus professor and former director of the Stanford University Mathematics Outreach Project in the Graduate School of Education, told Live Science. In other words, if the value of a function is, say, 7.5 at a certain point, then its slope, or derivative, at that point is also 7.5. And, “like pi, it comes up all the time in mathematics, physics and engineering,” Devlin said.Imaginary number i

The imaginary number i. (Image credit: Shutterstock)

Take the “p” out of “pi,” and what do you get? That’s right, the number i. No, that’s not really how it works, but i is a pretty cool number. It’s the square root of -1, which means it’s a rule breaker, as you’re not supposed to take the square root of a negative number.

“Yet, if we break that rule, we get to invent the imaginary numbers, and so the complex numbers, which are both beautiful and useful,” Eugenia Cheng (opens in new tab) , a mathematician at the School of the Art Institute of Chicago, told Live Science in an email. (Complex numbers can be expressed as the sum of both real and imaginary parts.)

The imaginary number i is an exceptionally weird number because -1 has two square roots: i and -i, Cheng said. “But we can’t tell which one is which!” Mathematicians have to just pick one square root and call it i and the other -i.

“It’s weird and wonderful,” Cheng said.i to the power of i

The number i raised to the power of i is actually a real number roughly equal to 0.207. (Image credit: Shutterstock)

Believe it or not, there are ways to make i even weirder. For example, you can raise i to the power of i — in other words, take the square root of -1 raised to the square root of -1 power.

“At a glance, this looks like the most imaginary number possible — an imaginary number raised to an imaginary power,” David Richeson, a professor of mathematics at Dickinson College in Pennsylvania and author of the book “Tales of Impossibility: The 2,000-Year Quest to Solve the Mathematical Problems of Antiquity (opens in new tab) ” (Princeton University Press, 2019), told Live Science. “But, in fact, as Leonhard Euler wrote in a 1746 letter, it is a real number!”

Finding the value of i to the i power involves rearranging Euler’s identity, a formula relating the irrational number e, the imaginary number i, and the sine and cosine of a given angle. When you solve the formula for a 90-degree angle (which can be expressed as pi over 2), you can simplify the equation to show that i to the power of i equals e raised to the power of negative pi over 2.

It sounds confusing (here’s the full calculation (opens in new tab) , if you dare to read it), but the result equals roughly 0.207 — a very real number. At least, in the case of a 90-degree angle.

“As Euler pointed out, i to the i power does not have a single value,” Richeson said, but rather takes on “infinitely many” values depending on the angle you’re solving for. (Because of this, it’s unlikely we’ll ever celebrate an “i to the power of i day.”)Belphegor’s prime number

Belphégor’s prime number, named after a demon, is a palindromic prime with a 666 hiding in the middle. (Image credit: Louis Le Breton/Dictionnaire Infernal)

Belphegor’s prime number is a palindromic prime number with a 666 hiding between 13 zeros and a 1 on each side. The ominous number can be abbreviated as 1 0(13) 666 0(13) 1, where the (13) denotes the number of zeros between the 1 and 666.

Although he didn’t “discover” the number, scientist and author Cliff Pickover (opens in new tab) made the sinister-looking number famous when he named it after Belphegor (or Beelphegor), one of the seven demon princes of hell in the Bible.

The number apparently even has its own devilish symbol, which looks like an upside-down symbol for pi. According to Pickover’s website, the symbol is derived from a glyph in the mysterious Voynich manuscript, an early-15th-century compilation of illustrations and text that no one seems to understand.2^{aleph_0}

There are many types of infinities, and 2^{aleph_0} is a number that describes the size of a particular infinite set.

Harvard mathematician W. Hugh Woodin (opens in new tab) has devoted many years of research to infinite numbers. It’s no surprise, then, that his favorite number is an infinite one: 2^{aleph_0}, or 2 raised to the power of aleph-naught, also called aleph-null. Aleph numbers are used to describe the sizes of infinite sets, where a set is any collection of distinct objects in mathematics. (So, for example, the numbers 2, 4 and 6 can form a set of size 3.)

As for why Woodin chose the number, he said, “Realizing that 2^{aleph_0} is not aleph_0 (i.e., Cantor’s theorem (opens in new tab) ) is the realization that there are different sizes of infinite. So that makes the conception of 2^{aleph_0} rather special.”

In other words, there’s always something bigger: Infinite cardinal numbers are infinite, so there is no such thing as the “largest cardinal number.”Apéry’s constant

Apéry’s constant is an irrational number that begins with 1.2020569 and continues infinitely and shows up in physics equations describing magnetism and the electron. (Image credit: Ian Cuming/Getty Images)

Harvard mathematician Oliver Knill (opens in new tab) told Live Science his favorite number is the Apéry’s constant (zeta(3)), “because there is still some mystery associated with it.” In 1979, French mathematician Roger Apéry proved that a value that would come to be known as Apéry’s constant is an irrational number. (It begins with 1.2020569 and continues infinitely.) The constant is also written as zeta(3), where zeta(3) is the Riemann zeta function when you plug in the number 3.

One of the biggest outstanding problems in math, the Riemann hypothesis, makes a prediction about when the Riemann zeta function equals zero and, if proven, would allow mathematicians to better predict how the prime numbers are distributed.

Riemann’s Zeta function. (Image credit: Furfur)

Of the Riemann hypothesis, renowned 20th-century mathematician David Hilbert once said (opens in new tab) , “If I were to awaken after having slept for a thousand years, my first question would be, ‘Has the Riemann hypothesis been proven?'”

So what’s so cool about this constant? It turns out that Apéry’s constant shows up in fascinating places in physics, including in equations governing the electron’s magnetism and orientation to its angular momentum.The number 1

The number 1 has many interesting properties, such as being the only number that is neither prime nor able to be factored into two numbers. (Image credit: Shutterstock)

Ed Letzter (opens in new tab) , a mathematician at Temple University in Philadelphia (and father of former Live Science staff writer Rafi Letzter), had a practical answer:

“I suppose this is a boring answer, but I’d have to choose 1 as my favorite, both as a number and in its different roles in so many different more abstract contexts,” he told Live Science.

One is the only number by which all other numbers divide into integers. It’s the only number divisible by exactly one positive integer (itself, 1). It’s the only positive integer that’s neither prime nor composite.

In both math and engineering, values are often represented as between 0 and 1: “100%” is just a fancy way of saying 1. It’s whole and complete.

And, of course, throughout the sciences, 1 is used to represent basic units. A single proton is said to have a charge of +1. In binary logic, 1 means yes. It’s the atomic number of the lightest element, and it’s the dimension of a straight line.Euler’s identity

Leonhard Euler was a Swiss mathematician, and his identity ties together three fascinating numbers: pi, natural log and i. (Image credit: Jakob Emanuel Handmann/Wikimedia Commons)

Euler’s identity, which is actually an equation, is a real mathematical jewel, at least as described by the late physicist Richard Feynman. It has also been compared to a Shakespearean sonnet.

In a nutshell, Euler’s identity ties together a number of mathematical constants: pi, natural log e and the imaginary unit i.

“[It] connects these three constants with the additive identity 0 and the multiplicative identity of elementary arithmetic: e^{i*Pi} + 1 = 0,” Devlin said.The number 0

Zero may have many useful properties, but it was a surprisingly late concept to emerge. (Image credit: Fernando Trabanco Fotografía/Getty)

If we’re already talking about how awesome 1 is, then why not throw in the even weirder and cooler number 0? For most of written human history, the concept of zero wasn’t all that important. Clay tablets from ancient Babylonian times didn’t always distinguish between numbers like 216 and 2106, according to the University of St. Andrews in Scotland (opens in new tab) . 

The ancient Greeks began to develop the idea of using zero as an empty place indicator to distinguish numbers of different magnitudes, but it wasn’t until roughly the seventh century that Indian mathematicians, like Brahmagupta, began describing the modern idea of zero. Brahmagupta wrote that any number multiplied by zero is zero, but he struggled with division, saying that a number, n, divided by zero just comes out as n/0, rather than the modern answer, which is that the result is undefined. (The Maya had also independently derived the concept of zero by A.D. 665.) 

Zero is extremely useful, but it is a very tricky concept for many people to wrap their heads around. We have examples such as 1 horse or 3 chickens in our day-to-day lives, but using a number to represent nothing is a larger conceptual leap. “Zero is in the mind but not in the sensory world,” the late Robert Kaplan, a Harvard math professor, told Vox (Kaplan died in 2021). Still, without 0 (and 1), we wouldn’t be able to represent all of the digital binary code that makes our contemporary world run. (Data on computers is represented by strings of 0s and 1s.)The square root of 2

This painting by Raphael depicts philosophers from the school of Athens, including Plato, Aristotle and Pythagoras, who was credited with discovering the square root of 2. (Image credit: mikroman6/Getty)

Perhaps the most dangerous number ever conceived, the square root of 2 supposedly led to the first mathematical murder in history. The Greek mathematician Hippasus of Metapontum is credited with discovering it in the fifth century B.C., according to the University of Cambridge (opens in new tab) . While working on a separate problem, Hippasus is said to have stumbled on the fact that an isosceles right triangle whose two base sides are 1 unit in length will have a hypotenuse that is √2, which is an irrational number. 

According to legend, Hippasus’ contemporaries, members of the quasi-religious order known as the Pythagoreans, threw him into the sea after hearing about his great discovery. That’s because the Pythagoreans believed that “all is number” and the universe only contained whole numbers and their ratios. Irrational numbers like √2 (and pi), which can’t be expressed as a ratio of whole numbers and go on forever after the decimal place, were seen as an abomination. 

These days, we’re a little calmer about √2, often calling it Pythagoras’ constant. It starts off as 1.4142135623 … (and, of course, goes on forever). ) Pythagoras’ constant has all sorts of uses. Besides proving the existence of irrational numbers, it is used by the International Organization for Standardization (ISO) to define the A paper size. The 216 definition (opens in new tab) of the A paper states that the sheet’s length divided by its width should be 1.4142. This means that a piece of A1 paper divided in half by width will yield two A2 pieces of paper. Divide an A2 in half again, and it will produce two A3 pieces of paper, and so on.Slice of pi

NASA uses a truncated estimate of pi that only includes 15 places after the decimal point. That’s all the agency needs to get everywhere they want to go in space. (Image credit: NASA/JPL)

Sometimes, the number cooler than pi is…a truncated version of pi. At least, that’s the case for NASA and scientists at the Jet Propulsion Laboratory (JPL) in California. For interplanetary navigation, JPL uses the number 3.141592653589793, according to JPL’s Chief Engineer for Mission Operations and Science, Marc Rayman (opens in new tab) . At that level of accuracy, Rayman said, NASA can get everything it builds wherever it needs to go.

To see why, it’s helpful to do some number-crunching. The most distant spacecraft from Earth is the Voyager 1 spacecraft, which is more than 14.6 billion miles (23.5 billion kilometers) distant from us. At this distance, you can calculate a circumference of a circle that is roughly 94 billion miles (more than 150 billion km) around, yet adding extra decimal places to pi only shaves off a half-inch (1.2 centimeters) of error from the calculation, Rayman said.

Even if scientists wanted to calculate the radius of a circle the size of the known universe to the accuracy of a width of a hydrogen atom, it would only need 37 digits after the decimal point to reach that accuracy, Rayman said.

So what’s cooler than pi? A slice of pi.

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Israel announces military operation expanding in Gaza to seize ‘large areas’

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Israel announces military operation expanding in Gaza to seize 'large areas'

Israel is beginning a major expansion of its military operation in Gaza and will seize large areas of the territory, the country’s defence minister said.

Israel Katz said in a statement that there would be a large scale evacuation of the Palestinian population from fighting areas.

In a post on X, he wrote: “I call on the residents of Gaza to act now to remove Hamas and return all the hostages. This is the only way to end the war.”

He said the offensive was “expanding to crush and clean the area of terrorists and terrorist infrastructure and capture large areas that will be added to the security zones of the State of Israel”.

The expansion of Israel’s military operation in Gaza deepens its renewed offensive.

The ceasefire between Israel and Hamas that had begun in January ended in March as Israel launched various air strikes on targets across Gaza.

The deal had seen the release of dozens of hostages and hundreds of Palestinian prisoners, but collapsed before it could move to phase two, which would have involved the release of all hostages and the withdrawal of Israeli forces from Gaza.

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26 March: Anti-Hamas chants heard at protest in Gaza

The Israel Defense Forces (IDF) had already issued evacuation warnings to Gazans living around the southern city of Rafah and towards the city of Khan Yunis, telling them to move to the al Mawasi area on the shore, which was previously designated a humanitarian zone.

Israeli forces have already set up a significant buffer zone within Gaza, having expanded an area around the edge of the territory that had existed before the war, as well as a large security area in the so-called Netzarim corridor through the middle of Gaza.

This latest conflict began when Hamas launched an attack on Israel on 7 October 2023, killing around 1,200 people and taking around 250 hostages.

The ensuing Israeli offensive has killed more than 50,000 Palestinians, according to Gaza’s Hamas-run health ministry.

Read more:
Father demands protection after Gaza aid workers’ deaths
Anti-Hamas chants heard at rare protest in Gaza

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Bodies of aid workers found in Gaza

Aid group Doctors Without Borders warned on Wednesday that Israel’s month-long siege of Gaza means some critical medications are now short in supply and are running out, leaving Palestinians at risk of losing vital healthcare.

“The Israeli authorities’ have condemned the people of Gaza to unbearable suffering with their deadly siege,” said Myriam Laaroussi, the group’s emergency coordinator in Gaza.

“This deliberate infliction of harm on people is like a slow death; it must end immediately.”

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UK

Heathrow bosses ‘warned about substation’ days before major power outage, MP committee hears

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Heathrow bosses 'warned about substation' days before major power outage, MP committee hears

Heathrow Airport bosses had been warned of a potential substation failures less than a week before a major power outage closed the airport for a day, a committee of MPs has heard.

The chief executive of Heathrow Airline Operators’ Committee Nigel Wicking told MPs of the Transport Committee he raised issues about resilience on 15 March after cable and wiring took out lights on a runway.

A fire at an electricity substation in west London meant the power supply was disrupted to Europe’s largest airport for a day – causing travel chaos for around 200,000 passengers.

“I’d actually warned Heathrow of concerns that we had with regard to the substations and my concern was resilience”, Mr Wicking said.

“So the first occasion was to team Heathrow director on the 15th of the month of March. And then I also spoke to the chief operating officer and chief customer officer two days before regarding this concern.

“And it was following a number of, a couple of incidents of, unfortunately, theft, of wire and cable around some of the power supply that on one of those occasions, took out the lights on the runway for a period of time. That obviously made me concerned.”

Mr Wicking also said he believed Heathrow’s Terminal 5 could have been ready to receive repatriation flights by “late morning” on the day of the closure, and that “there was opportunity also to get flights out”.

However, Heathrow chief executive Thomas Woldbye said keeping the airport open during last month’s power outage would have been “disastrous”.

There was a risk of having “literally tens of thousands of people stranded in the airport, where we have nowhere to put them”, Mr Woldbye said.

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What are Donald Trump’s tariffs, what is ‘liberation day’ and how does it all affect the UK?

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What are Donald Trump's tariffs, what is 'liberation day' and how does it all affect the UK?

If there is a word that has dominated Donald Trump’s second term, it’s tariffs. 

Aluminium, steel, cars and champagne have all been in his firing line, while China, Canada and Mexico are the countries targeted with the heaviest costs.

Along the way, there have been threats, pauses and postponements.

So what are tariffs, what is in the pipeline – and what could all this mean for the UK?

What are tariffs and why is Trump threatening to use them?

Tariffs are taxes on goods imported into the US.

It is the importers buying the goods who pay the tariffs – therefore, American companies.

Ultimately, the intent is to protect US manufacturing and bolster jobs by making foreign-made products less attractive.

However, there is a knock-on effect: to compensate for tariffs, companies put up their prices, so customers end up paying more for goods.

Tariffs can also damage foreign countries as they make their products pricier and harder to sell.

In his second term, Mr Trump has frequently used them – or the threat of them – as a trade weapon.

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Trump’s tariffs: What can we expect?

They are a key part of Mr Trump’s efforts to reshape global trade relations, and he plans to impose a swathe of what he calls “reciprocal” taxes that would match tariffs levied by other nations.

Tariffs were also part of his playbook in his first term, when he imposed taxes on most goods coming from China and used them as a bargaining chip to force Canada and Mexico to renegotiate a North American trade pact.

On his first day back in office, the US president promised 25% tariffs on all products coming into the US from its nearest neighbours Mexico and Canada – ostensibly to force the countries to tackle illegal migration and fentanyl crossing the border.

What is liberation day?

Mr Trump has branded 2 April “liberation day”, when he could unveil the reciprocal tariffs on countries deemed to be giving the US a bad deal on trade.

The extent of potential tariffs and countries affected remains unclear, with Mr Trump at times sending mixed messages.

On 30 March, he said “all countries” could expect to be hit by tariffs.

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What is Trump’s ‘Liberation Day’?

Speaking from Air Force One, the US president rubbished a question from a reporter who asked whether it was true he was planning on targeting between 10 and 15 countries.

“Who told you 10-15 countries? You didn’t hear it from me,” he said.

When pressed on how many he was planning to hit, he said: “You’d start with all countries, let’s see what happens.”

Two days prior, he said he was open to carving out deals with countries seeking to avoid US tariffs, but that those agreements would be negotiated after 2 April.

He had previously said he “may give a lot of countries breaks, but it’s reciprocal”, adding: “We might be even nicer than that.”

How could the UK be affected?

The UK hopes an economic deal with the US will spare the country from some of the tariffs.

Sir Keir Starmer and Mr Trump have had “productive negotiations” towards a UK-US “economic prosperity deal”, Downing Street has said.

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‘Everything on table over US tariffs’

The two leaders discussed a possible deal in a phone call on Sunday and agreed negotiations will “continue at pace”, according to a statement released on Sunday 30 March.

The day before the so-called “liberation day”, Sir Keir told Sky News political editor Beth Rigby the UK was “working hard on an economic deal” with the US and said “rapid progress” has been made.

But, he admitted: “Look, the likelihood is there will be tariffs. Nobody welcomes that, nobody wants a trade war.

“But I have to act in the national interest and that means all options have to remain on the table.”

Sir Keir added: “We are discussing economic deals. We’re well advanced.

“These would normally take months or years, and in a matter of weeks, we’ve got well advanced in those discussions, so I think that a calm approach, a collected approach, not a knee-jerk approach, is what’s needed in the best interests of our country.”

Mr Trump has not explicitly said the UK is in his sights for further tariffs, though he has described VAT – a tax added on all goods and services in the UK – as unfair.

In deciding what is a reciprocal tariff for the UK, it’s possible Mr Trump could use the tax, typically 20%, to decide.

Data shows no great trade imbalances – the gap between what you import and export from a certain country – and UK figures show no trade deficit with the United States.

UK ministers have previously suggested this could be good news for avoiding new levies.

But the tariffs Mr Trump has already announced would have a big impact on the UK – particularly the car tariff.

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Business secretary hopes Trump tariffs will be ‘reversed in weeks or months’

Jonathan Reynolds, the business and trade secretary, told Sky News he is “hopeful” the tariffs can be reversed soon.

He warned: “The longer we don’t have a potential resolution, the more we will have to consider our own position in relation to [tariffs], precluding retaliatory tariffs.”

He added the government was taking a “calm-headed” approach in the hope a deal can be agreed, but said it is only “reasonable” that retaliatory tariffs are an option, echoing Sir Keir’s sentiments over the weekend.

What tariffs have already been announced?

Some tariffs have already come into effect, while Mr Trump has confirmed some that will come in on 2 April.

He has said a 25% tariff on all cars imported to the US will come into effect, with a similar tariff on car parts expected to follow in May.

This could prove even more complicated for American car makers, who source components from around the world even if the vehicle is made in the US.

Trump tariffs teaser for SEO liberation day explainer

But Mr Trump has insisted the move will “continue to spur growth”, pointing to plans from Hyundai – the South Korean car maker – to build a $5.8bn (£4.5bn) steel plant in Louisiana.

The tariff could have a huge impact on the UK’s car industry, including on manufacturers such as Jaguar Land Rover, Aston Martin and Rolls-Royce.

Official data shows the US is the UK car sector’s largest single market by country, accounting for £6.4bn worth of car exports in 2023 – 18.4% of the total.

Trump has also said he will place a 25% tariff on all imports from any country that buys oil or gas from Venezuela, which includes the US itself – in addition to imposing new tariffs on the South American country.

On 12 March, a 25% tariff on all steel and aluminium imports to the US came into effect, affecting UK products worth hundreds of millions of pounds.

The move came after he placed a 10% tax on all imports from China, which he later doubled to 20%.

He placed 25% tariffs on Mexico and Canada, but paused them for a month two days after they came into effect, meaning they are set to resume on 2 April.

The pause did not fully cover a tariff of 10% on Canadian energy products.

What has been the global response to tariffs?

There has widely been condemnation of the tariffs, especially from countries worst affected like Mexico and Canada.

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Canadian PM: ‘Tariffs are an attack’

Some have imposed, or threatened to impose, retaliatory tariffs.

China has already hit back with retaliatory tariffs covering a range of US goods, including a 15% tariff on coal and liquefied natural gas products, a 10% tariff on US crude oil and tariffs of up to 15% on key US farm exports.

Canada imposed tariffs of its own on US products, including a 25% reciprocal tariff on US steel and aluminium products and tariffs worth an estimated C$29.8bn (£16bn) on a wide range of US products including orange juice, peanut butter, alcohol, coffee and clothing.

Read more on tariffs:
It may be harder for the UK to trump metals tariffs
Stock markets tumble as Trump tariffs loom

The European Union has said it will impose retaliatory tariffs on the US, but when they will come into force is unknown.

The European Commission initially threatened to impose “countermeasures” affecting €26bn (£21.9bn) of US goods from 1 April, but later delayed this until the middle of April.

The bloc said the delay was because it wanted “additional time for discussions” with the US after Mr Trump threatened a 200% tariff on EU alcohol – including wine and champagne – if the bloc imposed duties on US whiskey.

Any tariffs imposed by the bloc would not only impact US steel and aluminium products, but also textiles, home appliances, agricultural goods and whiskey.

Why tariffs could cost you – even if Trump spares UK

Even if no tariffs are put on all UK exports to the US, consumers globally will still be impacted by the wider trade war, particularly in the US.

Economists believe that tariffs will raise costs in the US, sparking a wave of inflation that will keep interest rates higher for longer. The US central bank, the Federal Reserve, is mandated to act to bring inflation down.

More expensive borrowing and costlier goods and services could bring about an economic downturn in the US and have knock-on effects in the UK.

Forecasts from the National Institute of Economic and Social Research (NIESR) predict lower UK economic growth due to higher global interest rates.

It estimated that UK GDP (a measure of everything produced in the economy) could be between 2.5% and 3% lower over five years and 0.7% lower this year.

The Centre for Inclusive Trade Policy thinktank said a 20% across-the-board tariff, impacting the UK, could lead to a £22bn reduction in the UK’s US exports, with the hardest-hit sectors including fishing and mining.

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