SOLVETUTORMATH SOLVER

Instrument MI-05-167 · Conversion

Length Converter

One metre is exactly 1250⁄381 feet — a rational number, fixed by treaty. This instrument applies the exact factors and shows every one.

Instrument MI-05-167
Sheet 1 OF 1
Rev A
Verified
Type 05 — Conversion SER. 2026-05167

Feet

3.280840

ft = m × 3.280839895…

39.370079 Inches
0.001000 Kilometres
0.000621 Miles
The working Every figure verified twice
  1. xFt = 1·3.28084 = 3.280840
  2. xIn = 1·39.370079 = 39.370079
  3. xKm = 1·0.001 = 0.001000
  4. xMi = 1·0.000621 = 0.000621
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

Every imperial length unit is, by definition, an exact decimal multiple of the metre. Since the 1959 international yard and pound agreement, one inch is 25.4 mm precisely — not approximately — and that cascades upward: a foot is 0.3048 m, a yard 0.9144 m, a statute mile 1609.344 m. Converting between the systems is therefore not measurement but arithmetic, and it can be done with zero error.

Run the definitions in reverse and the numbers stop terminating: one metre is 1 ÷ 0.3048 = 3.280839895013… feet and 1 ÷ 0.0254 = 39.370078740157… inches. These look irrational but are ordinary fractions — 1250⁄381 and 5000⁄127 — so their digits eventually repeat and carry no uncertainty at all. This sheet holds your entry internally in metres and multiplies by those factors at full double precision.

Because all four output factors descend from the same 0.3048 definition, they stay mutually consistent: the feet figure divided by 5280 reproduces the miles figure digit for digit, and the inches figure is always exactly twelve times the feet. If a printed conversion table ever disagrees with this instrument past the tenth digit, the table rounded first.

1 ft=0.3048 m1 in=2.54 cm1\ \text{ft} = 0.3048\ \text{m} \qquad 1\ \text{in} = 2.54\ \text{cm}1 mi=1609.344 m1\ \text{mi} = 1609.344\ \text{m}
m — the length in metres · ft, in, km, mi — the same length in feet, inches, kilometres, and statute miles. All four factors follow from 1 ft = 0.3048 m and 1 mi = 1609.344 m, both exact by the 1959 international yard and pound agreement.
  • Type your measurement into the Length field; 1 metre is preloaded as a reference.
  • Pick the unit you measured in — mm, cm, m, km, in, ft, yd, or mi — from the menu beside the field.
  • Read the four labelled results: Feet, Inches, Kilometres, and Miles, recomputed as you type.
  • Going imperial-to-metric? Set the input unit to ft, in, yd, or mi and read the Kilometres line for the metric value.

Worked example — one metre, four ways

Enter 1 and leave the unit on metres. The sheet returns 3.280840 feet, 39.370079 inches, 0.001 kilometres, and 0.000621 miles. The inch figure is the giveaway that these are definitions run backwards: 1 ÷ 0.0254 = 39.37007874…, an infinite decimal that is nevertheless the exact fraction 5000⁄127.

Scale it up and the exactness holds. Enter 1609.344 metres — one statute mile by definition — and the results read precisely 5280 feet, 63360 inches, and 1 mile, with nothing lost anywhere in the chain, because every factor descends from the same treaty definition of the foot.

Questions

Is a foot exactly 0.3048 metres?

Yes — exactly, by definition rather than by measurement. The 1959 international yard and pound agreement between six English-speaking standards bodies fixed the yard at 0.9144 m, which makes the foot 0.3048 m and the inch 25.4 mm with zero uncertainty. Every factor this sheet uses is derived from those definitions, so the only rounding you will ever see is in the displayed decimals.

Why is one metre such an awkward number of feet?

Because the definition runs the other way. The foot is defined as 0.3048 m, and dividing 1 by 0.3048 gives 1250⁄381 — a perfectly exact fraction whose decimal form, 3.280839895013…, never terminates. The number looks messy but carries no error; written as a fraction it is as tidy as the definition itself.

Is the mile here a statute mile or a nautical mile?

A statute mile — 5280 feet, exactly 1609.344 m. The nautical mile is a different unit, defined as exactly 1852 m and used in sea and air navigation because it approximates one minute of latitude. If you need nautical miles, divide the metre value by 1852; the two miles differ by about 15%.

How do I convert feet or inches back to metres?

Set the input unit menu to ft or in and type your figure — the instrument stores every entry in metres internally, so the Kilometres result gives the metric answer directly (multiply it by 1000 for metres). By hand: multiply feet by 0.3048 or inches by 0.0254; both factors are exact, so no error accumulates.

Is the US survey foot the same foot?

No — and the difference finally mattered enough that NIST and NOAA deprecated the US survey foot at the end of 2022. The survey foot is 1200⁄3937 m ≈ 0.304800610 m, about two parts per million longer than the international foot used here. Over a mile that is a third of a centimetre; over a state-wide coordinate grid, metres. New work uses the international foot only.

References