Speed Unit Converter: m/s, km/h, mph, ft/s, knots

Speed Unit Converter

Speed is how far something travels in a given amount of time. A speed unit converter rewrites a speed from one unit into another, such as kilometres per hour into miles per hour. This page converts between metres per second, kilometres per hour, miles per hour, feet per second and knots, and shows all five values at the same time.

What the converter does

A visitor types one number and picks the unit that number is written in. The page returns the same speed in all five units.

• Results are shown to eight significant figures. Only the display is rounded. The conversion runs on the number as typed.
• A result below 0.0001 in size, or of a billion or more, is shown in scientific notation. Zero is shown as a plain 0.
• Negative values are accepted. A speed measured along a chosen direction is signed, so a value below zero means motion the other way.
• An empty box produces a prompt rather than a number. A link carrying a unit the page does not offer produces a message rather than a conversion.

The five units

The metre per second is the SI unit: one metre of distance for every second of time. Each of the other four units is a fixed number of metres per second. None of those numbers is a measurement, so none of them changes over time.

Speed conversion formula

Every unit here is a fixed multiple of the metre per second, so a conversion is one multiplication and then one division. The value is carried into metres per second, then back out into the unit wanted:

$v_2 = \frac{v_1 \times k_1}{k_2}$

where $v_1$ is the speed typed in, $k_1$ is the number of metres per second in one unit of the chosen unit, $k_2$ is the number of metres per second in one unit of the wanted unit, and $v_2$ is the answer.

Nothing is added or subtracted along the way. All five scales read zero at the same speed, so only the size of the step changes. Temperature is the case where that is untrue: Celsius and Fahrenheit start counting at different points, so a converter that only multiplied would report 0 °C as 0 °F instead of 32 °F.

Where the four factors come from

An hour is 3,600 seconds and a kilometre is 1,000 metres, so the kilometre per hour is a ratio of two exact whole numbers:

$1\ \mathrm{km/h} = \frac{1\,000\ \mathrm{m}}{3\,600\ \mathrm{s}} = 0.2777\ldots\ \mathrm{m/s}$

The mile per hour rests on the international mile, which has been exactly 1,609.344 m since the International Yard and Pound Agreement of 1959:

$1\ \mathrm{mph} = \frac{1\,609.344\ \mathrm{m}}{3\,600\ \mathrm{s}} = 0.44704\ \mathrm{m/s}$

That one comes out even. The same 1959 agreement fixes the international foot at exactly 0.3048 m, which is the foot per second factor with no further arithmetic.

The knot is one nautical mile per hour. The international nautical mile has been exactly 1,852 m since the International Extraordinary Hydrographic Conference held at Monaco in 1929:

$1\ \mathrm{kn} = \frac{1\,852\ \mathrm{m}}{3\,600\ \mathrm{s}} = 0.51444\ldots\ \mathrm{m/s}$

All four figures are definitions rather than measurements, and all four are listed in NIST Special Publication 811, Appendix B.

Example: 100 km/h

A car travelling at 100 km/h covers 100,000 metres every 3,600 seconds. Carrying that into metres per second is the first step:

$v = \frac{100 \times 1\,000}{3\,600} = 27.7777\ldots\ \mathrm{m/s}$

Dividing that result by each of the other factors gives the rest. To eight significant figures the page shows 27.777778 m/s, 62.137119 mph, 91.134442 feet/s and 53.99568 kn.

The miles-per-hour answer is worth checking on its own, because it is the conversion people ask for most. One mile is 1.609344 km exactly, so 100 divided by 1.609344 gives 62.137119 mph. The rough version used in conversation, "about 62 mph", is that same number cut short.

Knots are not miles per hour

A nautical mile is 1,852 m and a statute mile is 1,609.344 m, so the nautical mile is the longer of the two. One knot is 1.1507794 mph. At 100 knots the page shows 115.07794 mph and 185.2 km/h, so reading a knot as a mile per hour understates the speed by about 15 percent.

The knot survives at sea and in the air because a nautical mile is close to one minute of latitude on a chart. A ship holding 10 knots for an hour has covered about ten minutes of latitude, which is a useful thing to read straight off the chart.

Common speed conversions

Each row below is the value one unit produces in the other four, at eight significant figures.

Which values are exact and which are rounded

Two of the four factors are exact decimals, and the other two are exact fractions whose decimals never end.

• 1 mph is exactly 0.44704 m/s. The mile is exactly 1,609.344 m and the hour is exactly 3,600 s, and that division comes out even.
• 1 foot/s is exactly 0.3048 m/s. The international foot is exactly 0.3048 m, from the same 1959 agreement.
• 1 km/h is exactly 1,000 metres per 3,600 seconds. As a decimal that is 0.27777… with the 7 repeating for ever, so any decimal written for it has been cut short.
• 1 kn is exactly 1,852 metres per 3,600 seconds. As a decimal that is 0.51444… with the 4 repeating.

The converter stores the two repeating factors as divisions rather than as shortened decimals, so the rounding a reader sees comes from the display and not from the constants. Eight significant figures is wide enough to show a defining value in full and narrow enough to hide the last digits of the computer's arithmetic, which carry rounding noise rather than information. The 100-knot answer above is one example: the exact figure is 185.2 km/h, the arithmetic lands a hair away from it, and the display shows 185.2.

Frequently asked questions

How many mph is 100 km/h? 62.137119 mph at eight significant figures, usually quoted as 62.1 mph. The reverse case is close to a mirror image: 100 mph is 160.9344 km/h, exactly.

How is m/s converted to km/h? Multiply by 3.6. A metre per second covers 3,600 m in an hour, which is 3.6 km, and that factor is exact. Dividing by 3.6 goes the other way.

Is a knot the same as a mile per hour? No. A knot is one nautical mile per hour, and a nautical mile is 1,852 m against the statute mile's 1,609.344 m. One knot is 1.852 km/h exactly, or 1.1507794 mph.

Why is 60 mph exactly 88 feet/s? Because both units are defined from the same 1959 feet. A mile is 5,280 feet, so 60 miles is 316,800 feet, and an hour is 3,600 seconds. That division leaves exactly 88, with no rounding anywhere in it.

Can a negative speed be converted? Yes. A speed measured along a chosen direction is signed, so a negative value describes motion the other way. The page converts it instead of refusing it.

Which unit is used where? The metre per second is the SI unit and is standard in science. Kilometres per hour appear on road signs in most countries, and miles per hour in the United States and the United Kingdom. Feet per second are common in United States engineering and in ballistics. Knots are used at sea and in aviation.