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Metric ↔ imperial without a calculator

Drawings come in millimetres, the tape is in sixteenths, the box is labelled in both, and the person on the other end of the phone is thinking in feet. You will convert all day. Two exact numbers do all of it, and two rough ones let you do most of it in your head while you decide whether the exact one is even needed.

Two exact numbers, two rough ones

  • 1" = 25,4 mmexact. Inches × 25.4 → mm. mm ÷ 25.4 → inches.
  • 1 ft = 0,3048 mexact. Feet × 0.3048 → m. m ÷ 0.3048 → feet.
  • rough: 1" ≈ 25 mm4" ≈ 100 mm. Off by 1.6% — fine for deciding, not for cutting.
  • rough: 1 m ≈ 3.3 ftor 10 ft ≈ 3 m. Off by 1.6% the other way.

The direction is the thing people get wrong, not the number. Going from a big unit to a small one, the count gets bigger: inches to millimetres, multiply. Going from small to big, the count gets smaller: millimetres to inches, divide. Say which way the number should move before you do anything and you will not divide when you meant to multiply.

Three worked examples

1. A 600 mm box opening — will a 2-foot panel fit?

  1. Rough first: 2 ft is 24", and 24 × 25 ≈ 600 mm. It is right on the line, so rough is not enough — go exact.
  2. 24 × 25,4 = 609,6 mm.
  3. The panel is 609.6 mm; the opening is 600. It does not fit — by nearly 10 mm. That is what the rough version was hiding.

2. 1,350 mm on a drawing — what is that on the tape?

  1. Small unit to big: divide. 1350 ÷ 25.4.
  2. Rough: 1350 ÷ 25 = 54, so a bit less than 54". Exact: 53.15".
  3. 0.15" is between 2/16 (0.125) and 3/16 (0.1875), nearer 2/16. 53 1/8", near enough 53 3/16" — say which sixteenth you are calling it and stick to it.
Turning the decimal into a sixteenth

Multiply the decimal part by 16: 0.15 × 16 = 2.4 sixteenths. Round to 2: 2/16 = 1/8. The fraction / decimal drill is that move on its own.

3. A 30 m cable run — how many feet?

  1. Metres to feet: the count gets bigger, so divide by 0.3048 (or multiply by 3.281 — same thing).
  2. Rough: 30 × 3.3 = 99, so about a hundred feet.
  3. Exact: 30 ÷ 0.3048 = 98.4 ft. The rough answer was within a foot, which for ordering cable is usually the number you wanted anyway.
Try one: 18" to millimetres

Rough: 18 × 25 = 450. Exact: 18 × 25.4 = 457.2 mm. The rough answer was 7 mm short — more than a quarter inch.

Drill it

Inches to millimetres, millimetres to inches, feet to metres, metres to feet — mixed. Within half a percent counts on the multiplications, one percent on the divisions, so a sensible rounding is fine.

Série 0 Record 0

Cet exercice a besoin de JavaScript pour générer et corriger les questions. Activez-le pour vous exercer — l’explication ci-dessous fonctionne dans les deux cas.

Questions fréquentes

Is an inch exactly 25.4 mm?

Yes — exactly, by definition, since 1959. That is why every conversion on this site multiplies or divides by 25.4 and nothing else. A foot is 12 of those, so 304.8 mm, or 0.3048 m.

When is the rough conversion good enough?

When you are deciding, not cutting. "About 2.5 cm to the inch" tells you whether a 600 mm box will fit a 2-foot gap (it will, just). It does not tell you where to cut a pipe. For anything you measure to the sixteenth, use 25.4 and keep a decimal.

Which way is the mistake usually made?

Dividing when you should multiply. Going to millimetres the number gets bigger, so multiply by 25.4; coming back to inches it gets smaller, so divide. Say the direction out loud before you touch the calculator — the drill marks that exact slip.

Voir aussi

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