SOLVETUTORMATH SOLVER

Instrument MI-05-114 · Conversion

Height Converter

Forms want feet and inches; clinics record centimetres. Enter a stature once and read it as decimal inches, feet plus inches, and centimetres.

Instrument MI-05-114
Sheet 1 OF 1
Rev A
Verified
Type 05 — Conversion SER. 2026-05114

Inches

67.72

in = m ⁄ 0.0254

5 Whole feet
7.7 …plus inches
172.0 Centimetres
The working Every figure verified twice
  1. hIn = 1.72 ⁄ 0.0254 = 67.72
  2. hFt = floor(1.72 ⁄ 0.3048) = 5
  3. hRemIn = (1.72 ⁄ 0.3048 − floor(1.72 ⁄ 0.3048))·12 = 7.7
  4. hCm = 1.72·100 = 172.0
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Height is the one everyday measurement still quoted in two rival systems at once. Medical records and most of the world use centimetres; the United States, British conversation, and nearly every online form use feet and inches. Since the 1959 international yard and pound agreement the two systems have been locked together exactly — one inch is 25.4 mm by definition — so moving between them is pure arithmetic, with no measurement error anywhere in the chain.

The only real work is the mixed-radix step. Feet-and-inches is not decimal notation: 5.64 ft and 5 ft 7.7 in are the same stature written two ways. The instrument divides your entry by 0.3048 to get decimal feet, keeps the whole-number part as the feet figure, and multiplies the remainder by 12 to recover the leftover inches — the same division-with-remainder used for turning minutes into hours, applied to length.

One caution at the edges: the remainder is rounded to one decimal for display, so a stature a hair under a whole foot — say 182.8 cm, which works out to 5 ft 11.97 in — sits closer to 6 ft than the feet figure alone suggests. When a form wants whole inches, round the single decimal-inches result instead; it is the number the other figures are derived from.

in=cm2.54ft=cm30.48\text{in} = \frac{\text{cm}}{2.54} \qquad \text{ft} = \frac{\text{cm}}{30.48}
m — the height in metres, the sheet's internal unit · in — the same height in decimal inches · ft — the whole-feet part · rem — the leftover inches after the whole feet are removed · cm — centimetres. Both divisors are exact: 1 in = 0.0254 m and 1 ft = 0.3048 m by the 1959 international definition.
  • Type the stature into the Height field — 172 cm is preloaded as a reference.
  • Pick the unit you measured in from the menu beside it: cm, m, in, or ft.
  • Read Inches for the single-number form, and Whole feet with '…plus inches' for the mixed form.
  • The Centimetres line gives the metric figure whenever your entry was imperial.

Worked example — 172 cm onto a US form

A passport application wants feet and inches; the clinic letter says 172 cm. Divide by 2.54: 172 ⁄ 2.54 = 67.7165, which the sheet displays as 67.72 inches. Divide by 12 for the mixed form: 67.72 ⁄ 12 = 5 remainder 7.7 — so 172 cm is 5 ft 7.7 in, exactly what Whole feet and '…plus inches' read.

The cross-check runs cleanly in reverse. Five whole feet are 5 × 30.48 = 152.4 cm, and the leftover 7.7165 inches are 7.7165 × 2.54 = 19.6 cm; added together they return 172.0 cm on the nose — no rounding residue, because every factor in the chain is exact by definition.

Questions

How many feet and inches is 172 cm?

5 ft 7.7 in. Divide 172 by 2.54 to get 67.72 inches, take out five whole feet (60 inches), and 7.7 remain. If a form insists on whole inches, 172 cm rounds to 5 ft 8 in — a figure that overstates the true stature by about three quarters of a centimetre.

Is one inch exactly 2.54 centimetres?

Exactly, by definition rather than by measurement. The 1959 international yard and pound agreement fixed the yard at 0.9144 m, which makes the foot 0.3048 m and the inch 25.4 mm with zero uncertainty. Converting a height therefore introduces no error at all — the only rounding you will ever see is the display trimming decimals.

Why show whole feet plus inches instead of decimal feet?

Because that is how the imperial world writes stature — nobody says 5.64 feet. Feet-and-inches is a mixed-radix notation, base twelve in its lower digit, like hours and minutes. The sheet does the remainder arithmetic for you: the whole-feet line is the floor of the decimal feet, and the '…plus inches' line is the remainder times 12, so the two always recombine to the exact figure.

How do I convert 5 ft 8 in back to centimetres?

Collapse the mixed figure into total inches first: 5 × 12 + 8 = 68. Enter 68 with the unit menu set to in, and the Centimetres line reads 172.7 cm. By hand, multiply total inches by 2.54. The instrument accepts plain feet too, but a mixed entry must become one number before it goes in.

Is 5 ft 7.7 in the same as 5.7 feet?

No — and the near-miss trips people constantly. 5 ft 7.7 in equals 5 + 7.7 ⁄ 12 = 5.64 decimal feet, while 5.7 decimal feet is 5 ft 8.4 in. The digits after the feet count twelfths, not tenths. When precision matters, work in a single unit — inches or centimetres — and split into feet only at the very end.

References