Numbers Worth Knowing for Estimation: A Pocket Set of Anchors

Every good estimate starts from a number you already know. Nobody can tell you offhand how many litres it takes to flood a football pitch, but anyone who knows the size of a pitch and the weight of a litre of water can work it out in a minute. The skill is less about arithmetic than about having the right few dozen numbers to start from.

This is our pocket set, the figures that turn up again and again in the working behind What's Your Guess? and in everyday back-of-the-envelope sums. Each is rounded to something easy to carry. They are deliberately rough: within a few per cent is plenty when the aim is to land within ten times.

A useful anchor has three parts: one or two significant figures, the right power of ten, and a rough sense of when it was true. "About 8.3 billion people, as of the mid-2020s" is a better memory than a ten-digit figure, because it is easy to recall, easy to multiply and honest about drifting.

When you learn a new figure, say it in powers of ten too. Knowing that the Earth's circumference is 4 × 10⁴ km makes it simple to combine with anything else, since multiplying becomes adding exponents.

• The world: about 8.3 billion people.
• India and China: about 1.4 billion each, with India now slightly ahead.
• The European Union: about 450 million.
• The United States: about 340 million.
• The United Kingdom: about 69 million.
• London and New York City: roughly 9 million and 8.5 million.
• Births worldwide: roughly 130 million a year.
• Life expectancy worldwide: about 73 years at birth.
• Household size: about 2.5 people in the US and 2.4 in the UK.

Populations grow, so these drift by a per cent or so a year. For estimates that is nothing, but check before you quote one as a fact.

• Around the Earth at the equator: about 40,000 km. The metre was originally defined so that the distance from the North Pole to the equator would be 10 million metres, which is why the distance round the Earth comes out so round.
• The Earth's diameter: about 12,700 km.
• The Earth's surface: about 510 million square km, of which about 71% is ocean.
• The Moon: about 384,000 km away on average.
• The Sun: about 150 million km away; its light takes about 8 minutes 20 seconds to reach us.
• The speed of light: about 300,000 km a second.
• Mount Everest: 8,849 metres.
• The ocean: about 3.7 km deep on average, and about 11 km at its deepest.
• An airliner: cruises about 10 to 12 km up at about 900 km an hour.

• A day: 1,440 minutes, or 86,400 seconds.
• A year: 8,760 hours, or about 31.6 million seconds. A handy way to remember the seconds is π × 10⁷, which is within half a per cent.
• A working year: about 2,000 hours, at 40 hours a week for 50 weeks.
• A long life of 80 years: about 29,000 days, or about 700,000 hours.

Time is the best tool there is for feeling the size of a big number, because everyone has lived through days and years. How a million seconds compares with a billion is the start of why big numbers are hard to grasp.

• An adult: about 1.7 m tall and about 70 kg, as round working figures.
• Blood: about 5 litres in an adult.
• Water: about 60% of an adult's body weight.
• Food energy: about 2,000 to 2,500 kilocalories a day.
• Walking pace: about 5 km an hour, with each step about three quarters of a metre.
• Sleep: roughly a third of a life.

• Water: a litre weighs a kilogram, and a cubic metre holds 1,000 litres and weighs a tonne. This one link between volume and weight opens up a huge number of questions about filling things.
• An Olympic swimming pool: 50 m by 25 m and at least 2 m deep, so at least 2,500 cubic metres, or 2.5 million litres.
• A football pitch: about 105 m by 68 m, a little over 7,000 square metres.
• A car: about 4.5 m long and about 1.5 tonnes.
• An elephant: roughly 3 to 6 tonnes, depending on the species and the animal.
• The Eiffel Tower: 330 m tall and about 10,000 tonnes.
• The Burj Khalifa: 828 m, the tallest building in the world.
• A smartphone: a little under 200 grams.
• A credit card: 85.6 mm by 54 mm, the same size the world over, which makes it a ruler in your pocket.

• The world economy: a little over $110 trillion a year, or roughly $14,000 for each person alive.
• The US economy: about $30 trillion a year.

Money figures go stale fastest, through growth and inflation both, so treat them as orders of magnitude rather than facts.

Anchors do their work in three ways.

Chaining. Multiply anchors and assumptions together, keeping the units beside each figure. How much water would it take to cover a football pitch 1 cm deep? 7,000 square metres × 0.01 m is 70 cubic metres. At 1,000 litres a cubic metre that is 70,000 litres, and at a tonne a cubic metre it weighs 70 tonnes. Two anchors and one assumption, and you can answer three questions.

Scaling. When you know one thing and need another like it, scale by the ratio. If you know a country's population and want a city's, ask what fraction of the country lives there. If you know the weight of a car and want a lorry's, ask how many cars long and wide it is. Ratios are often easier to judge than totals.

Checking. Use an anchor to test a result. Divide a total by the world's population and see whether the amount per person is believable. Convert a big number of seconds into years. If an estimate of a country's bread sales works out at ten kilograms of bread a person a day, you know a piece is wrong before you look for it. We go further into this in how to check a number.

The best list is one you made, because you will remember why each number is there. Two habits build it quickly.

First, after every question in What's Your Guess? where you were far off, open How it adds up and look at the figures in the working. Somewhere in there is usually the number you were missing: how tall a building is, how heavy an animal is, how many people use something. Write it down, rounded.

Second, retire numbers. A figure you learned ten years ago for a population, a price or a company's size may be well out by now. An anchor you no longer trust is worse than none, because it gives you false confidence. Refresh the ones that move, and keep the ones that do not, such as the size of the Earth, the speed of light and the weight of a litre of water, for life.