Rule of thumb · ComputersNº 76 / 167

2¹⁰ ≈ 10³

Every 10 bits multiplies by ~1,000 — kibi and kilo differ by just 2.4%.

Why it works

2¹⁰ = 1,024. So 2²⁰ ≈ a million, 2³⁰ ≈ a billion — powers of two estimated in your head to within a few percent.

When it fails

The 2.4% error compounds: by the fourth power it is 10%, so a 'terabyte' drive of 10¹² bytes shows as 931 GiB in an operating system counting in 2⁴⁰. That gap is not the manufacturer cheating, and it grows every time storage gets bigger.

How wrong is it?

At 10 the rule says 1,000 and the exact answer is 1,024 — 2.3% low. It holds to within 5% up to 21.6, then drifts.

+5%0−5%104580Powers of two

The 2.4% gap at 2^10 is the same 2.4% every ten powers, so it compounds: it is exactly why a "1 TB" drive shows up as 931 GB.

The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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Why is a kilobyte 1024 and not 1000?

Every 10 bits multiplies by ~1,000 — kibi and kilo differ by just 2.4%. 2¹⁰ = 1,024.

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