Fractions du ruban à mesurer
Every result on this site is a tape reading first and a decimal second — "8 1/2 in (8.49)" — because that is the order you need them in at the bender. This page is the arithmetic behind that: how the tape is cut up, how to get from a decimal to the right little line, how to add a shrink to a measurement without losing a sixteenth, and a drill that keeps setting new ones until it is reflex. Conduit numbers only; there is no general converter here.
Working in metric? Every calculator on the site works in millimetres too — flip the Imperial/Metric switch at the top of the page — and then there are no fractions at all. The metric tape section below is the whole of it.
How a tape is marked
An inch is cut into sixteen. The lines are different heights so you can tell which one you are on without counting: the tallest inside line is the half, the next two are the quarters, then four eighths, and the eight shortest are the odd sixteenths. Read the height first, then the position.
The odd sixteenths are the ones that catch people: 7/16 is the short line right after 3/8, 13/16 is the short line right after 3/4. If you find yourself counting all the little lines from zero, stop, find the nearest tall line you know, and count one or two from there.
Decimal to sixteenths
Keep the whole inches. Take the part after the point, multiply it by 16, round to the nearest whole number, and that is how many sixteenths. Then reduce if you can.
decimal part × 16 → round → sixteenths → reduce
| Calculator says | × 16 | Rounds to | Sur le ruban |
|---|---|---|---|
| 0,268 | 4,29 | 4/16 | 1/4 |
| 0,414 | 6,62 | 7/16 | 7/16 |
| 5,23 | 3,68 | 4/16 | 5 1/4 |
| 8,49 | 7,84 | 8/16 | 8 1/2 |
| 13,06 | 0,96 | 1/16 | 13 1/16 |
| 1,61 | 9,76 | 10/16 | 1 5/8 |
Why not go finer? 0.268 is closer to 17/64 than to 1/4, and it does not matter: a 64th is thinner than a pencil line, and the bend itself moves more than that when the pipe springs back after the pull. A sixteenth is the finest thing you can lay out and the finest thing worth laying out. That is why every result on the site rounds to it and shows the decimal small underneath — the decimal is for checking, the fraction is for marking.
Adding across a mark
Adding a shrink to a measurement is the fraction sum you do most. Put both numbers in sixteenths, add, then reduce. Do not try to add quarters to eighths in your head — go to sixteenths every time and the mistakes stop.
When the sixteenths pass 16, carry one inch and keep the rest — the third line beside. The same going the other way: to take a shrink off (you will, when you measure back from a fixed end), borrow an inch as 16/16 when you need to.
- 5 1/4 + 3/8 → 5 and 4/16, plus 6/16 → 5 and 10/16 → 5 5/8
- 12 + 1 5/8 → 13 5/8 (nothing to carry)
- 9 7/8 + 1/4 → 9 and 14/16, plus 4/16 → 9 and 18/16 → 10 and 2/16 → 10 1/8
- 27 3/16 + 1 5/8 → 27 and 3/16, plus 1 and 10/16 → 28 and 13/16 → 28 13/16
Feet and inches
Twelve inches to the foot. The calculators take feet-inches typed the
way you would say it — 1' 3 1/2", 1'3-1/2,
2ft 6 — and give the answer back in inches, because marks
along a stick of pipe are easier in plain inches. 1' 3 1/2" is 15 1/2 in;
a 3' 2 5/8" run is 38 5/8 in. To go back the other way, take out
twelves: 38 5/8 → 3 feet (36) with 2 5/8 left → 3' 2 5/8".
Reading a metric tape
A metric tape is marked in millimetres: a short line every millimetre, a taller one at each 5, and a numbered line every 10 (a centimetre). Most read the numbers in centimetres along the blade and every metre in red; on a job, say and write it all in millimetres — 1 245, not 124.5 cm — so nobody has to guess the unit.
That is why bending in millimetres needs no fractions. A millimetre is already about as fine as a pencil line, so the calculators round every mark to the whole millimetre and there is nothing to reduce and nothing to carry. Adding a shrink is plain addition: 1 245 + 38 = 1 283. Switch the site to Metric and every result reads that way. If you ever need to move between the two, 25.4 mm is one inch exactly — but type in the unit your tape reads and let the site convert.
The drill
Three kinds of question. Type the answer the way a tape reads — 8 1/2, or 1' 3 1/2" — or as a decimal if the question asks for one. A sixteenth either way counts.
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Questions
- Why does the site round to a sixteenth and not a 32nd or 64th?
- Because a sixteenth is the finest line on a working tape and about the width of a pencil mark. Anything finer is precision the bender cannot use — springback alone moves a bend more than a 64th. The decimal is shown small under every result for the times you want it.
- How do I turn 0.268 into a tape reading?
- Multiply the decimal by 16 and round: 0.268 × 16 = 4.3, so 4 sixteenths, which reduces to 1/4. The same for any decimal: the whole inches stay, the part after the point becomes sixteenths.
- What is 5 1/4 plus 3/8?
- Put both in sixteenths: 5 1/4 is 5 and 4/16, 3/8 is 6/16. Add: 5 and 10/16, which reduces to 5 5/8. Adding shrink to a measurement is exactly this every time.
Where this is used
Every calculator on the site: the offset gives between-marks and shrink as tape fractions, the saddle its centre-to-outer distance, the stub-up its mark from the end. If you are new to all of it, the six lessons on Bending, from zero end with this page's rule.