Estimation Didn’t Have to Be This Hard

An estimate is a quick calculation on friendly numbers with its assumptions on show. Aim only as close as the decision needs (within 10%, a factor of 2, or a factor of 10), measure misses as factors, and let the estimate catch the big mistakes.

The leading digit carries almost all of a number's size, so round to one significant figure and do the arithmetic on that. Keep two digits when the number starts with 1 or 2, lean your roundings different ways in a product, and round the big items carefully in a sum.

Every number sits on a powers-of-ten ladder, and its rung is its order of magnitude. Write big and small numbers as a digit times a power of ten, multiply by adding exponents and divide by subtracting them, and when you're unsure across a wide range, aim for the middle rung.

Translate big numbers into time, distance, weight or money per person. A million seconds is about 11.6 days and a billion is about 31.7 years, so a million and a billion differ the way a vacation differs from a career; dividing by the people involved catches the million–billion slip.

Reshape every sum until it's easy: multiply leading digits and count the zeros, halve one number and double the other, go through 10 or 100 for 5, 25 and 1%, step to a round number and correct, and nudge a divisor to a friendly neighbor. In a product, balance your roundings; in a division, move both numbers the same way.

A question nobody can look up is made of pieces anybody can guess; write them as a chain, multiply, say what you assumed, and check the answer by a second route that starts somewhere else.

Carry a dozen numbers you trust, from your own body, your home, the clock and a few sourced world facts, and build every other number from them.

When you don't know a number, name a low and a high you're sure of and take the geometric middle, the number the same factor from both; then narrow it with a quick look.

In a chain of honest guesses, some come out high and some low, so the errors mostly cancel and the answer usually lands far closer than the worst case; leaning guesses, repeated guesses and one wild piece are what break this.

Carry the units with every number and multiply by conversion factors that equal one, arranged so the units you don't want cancel; if the unit comes out right the arrangement is right, and if it comes out as nonsense you've found your mistake.

A time is an amount divided by a rate, and a habit is a daily time multiplied by the days; minutes a day times six is about hours a year, a mile on foot is about twenty minutes, and a line takes the people ahead divided by the people served each minute.

Most money questions are conversions: put prices in the same unit (per item, per day, per hour, per year) before comparing, multiply small differences by how often they happen, and use 72 divided by a yearly percentage for the doubling time.

Area is length times width and volume is area times depth, with every length in the same unit; then divide by what one unit covers or holds (the coverage on the can, say 350 square feet a gallon of paint, 27 cubic feet a cubic yard, about 7.5 gallons a cubic foot) and allow for the gaps.

To count what's too many to count, count a fair sample carefully, find how many samples make the whole, and multiply; crowds are area divided by about 10, 4.5 or 2.5 square feet a person, and a count "at once" is not a count "over the day".

Ten doublings is about a thousand (2¹⁰ = 1,024), so count the doublings and add three zeros for every ten; 72 divided by a growth rate gives the doubling time, halving is a little quicker than the same rule says, and doubling always looks slow right up until it doesn't.

Divide a big claim by the people, days or hours it's spread across until it's an amount you've seen yourself, then ask whether you'd believe that: plausible, possible but rare, or implausible.

Some numbers break limits that come with the numbers themselves: a drop can't pass 100%, shares of a whole can't pass 100%, an average sits inside its range, a part can't exceed its whole, and a day has 24 hours; when one does, look for the true number behind it.

Give a low, a high and a best guess; combine ranges end with end (lows with lows, highs with highs; for subtraction the ends cross), take the middle of a product range from the geometric middle (for narrow ranges, multiplying the plain middles lands close), and let overlapping ranges tell you what to measure next.

Break a project into pieces, estimate each as amount × rate with a low, likely and high, add what happens in a row, take the longest of what happens side by side, and correct the total with your own track record.

Size a market twice, once top-down from the people (people × share who buy × how often) and once bottom-up from the sellers (sellers × sales each), take the middle, and check the answer per person. Watch for the missing step, and use a ceiling when a plan looks too big.

The biggest questions about the planet break into a few anchors and a guess or two: the air's weight is the pressure on a square inch times the square inches, the oceans are area times depth. Work them with powers of ten, then check against the published value and see which guess cost the most.

Ten habits tie the book together: decide how rough is enough, one digit and some zeros, powers of ten, split it up, carry anchors, bound it and take the middle, let the units check you, per person per day, give a range, and check by a second route. Start with three and the rest follow.