The 5.10 mistake: why decimal height conversions go wrong

Two numbers that look the same

Five feet ten inches is 177.8 cm. The decimal 5.10 feet is 155.45 cm. The notation differs by a single character and the answers differ by 22 centimetres — enough to change a clothing size, a passport entry or a medical chart.

Where the error comes from

Feet and inches use a mixed radix. The inches column counts to twelve and then rolls over, so the fractional part of a height in feet is not the inches figure. Ten inches is ten twelfths of a foot, which is 0.833 feet, not 0.10.

Written correctly, it is 5′10″ — a prime for feet, a double prime for inches. The decimal point has no place in it.

The correct method

1. Multiply the feet by 30.48 — five feet gives 152.4 cm.
2. Multiply the inches by 2.54 — ten inches gives 25.4 cm.
3. Add them: 177.8 cm.

Going the other way

Divide the centimetres by 2.54 for total inches, then split that total into twelves. 180 cm gives 70.87 inches; five twelves make 60, leaving 10.87 — so 180 cm is 5 feet 10.9 inches, normally written 5′11″.

Where it actually bites

Spreadsheets. A column of heights entered as 5.10, 5.11, 6.0 sorts and averages as ordinary decimals, so 5.11 appears taller than 6.0 and every average is wrong. Store height in centimetres and format for display instead.

How the error spreads through data

The 5.10 problem rarely stays a personal mistake. It gets typed into a form, exported to a spreadsheet, and from there into a report that somebody makes a decision on. Because the values look like valid numbers, nothing flags them.

Sorting is where it surfaces first. A column containing 5.9, 5.10 and 5.11 sorts as 5.9, 5.10, 5.11 numerically — which puts 5 feet 9 inches below 5 feet 10 inches correctly by accident, then breaks the moment 5.9 is meant to be 5 feet 9 inches and is read as 5.90 feet. Averages are worse: the mean of 5.10 and 6.0 comes out at 5.55, a figure that corresponds to no real height at all.

Store metric, display imperial

The fix used by every system that handles this well is to store a single metric number and format it for display:

• Store height as an integer in centimetres, or as total inches if the audience is American.
• Compute on the stored value — averages, percentiles and sorting all behave correctly.
• Format only at the point of display, converting to feet and inches for the reader.

This is the same principle used for currency, where amounts are stored in minor units rather than as decimal strings. Mixed-radix values do not belong in a numeric column.

The rounding question

Converting 180 cm gives 70.87 inches, which is 5 feet 10.87 inches. Round to the nearest inch and you get 5′11″; truncate and you get 5′10″. Both appear in the wild, which is why two profiles for the same person can differ by an inch without either being wrong.

Our own convention is to round to the nearest whole inch for display and to keep the exact centimetre figure underneath. Where the difference matters — a height requirement with a hard cut-off, for instance — we show the unrounded value.

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The takeaway

Write the prime marks, keep the parts separate when you convert, and store centimetres in anything that will later be sorted or averaged.