Speed Converter

How speed units are defined

A speed is a distance divided by a time, so every speed unit is built from a length unit and a time unit. Both halves are defined exactly, which makes every factor in this converter exact as well:

• Kilometers per hour: 1,000 m in 3,600 s, so 1 m/s = 3.6 km/h exactly.
• Miles per hour: since 1959 a mile has been exactly 1,609.344 m, so 1 mph = 1.609344 km/h = 0.44704 m/s exactly.
• Knots: one nautical mile (exactly 1,852 m) per hour, so 1 kn = 1.852 km/h exactly. Ships and aircraft use knots.
• Feet per second: 0.3048 m per second, so 1 ft/s = 1.09728 km/h, and 60 mph is exactly 88 ft/s.

Mach is different. A Mach number is a speed divided by the speed of sound in the air around the object, and the speed of sound depends on air temperature. Mach 1 is about 340 m/s in air at 15 °C but nearer 295 m/s in the −56.5 °C air where airliners cruise. This converter uses one stated reference: the speed of sound at sea level in the standard atmosphere, 340.294 m/s. Treat its Mach figures as “Mach at 15 °C”, not as the Mach number an aircraft instrument would show at altitude.

The conversion formula

Converting a speed means multiplying by the ratio of the two unit sizes:

value

the speed you enter

size

one unit expressed in km/h, e.g. 1.609344 km/h for 1 mph and 1.852 km/h for 1 knot

The working states each unit in kilometers per hour because every definition is a short exact decimal there. In meters per second, 1 km/h would be 0.2777… m/s and 1 knot 0.51444… m/s, both repeating. When the factor in one direction is a clean number, the calculator uses it: km/h to mph divides by 1.609344 rather than multiplying by the rounded 0.621371…

For Mach the formula is the same with the reference speed of sound as the unit size: Mach = speed in m/s ÷ 340.294.

Worked examples

100 km/h to mph. A mile per hour is 1.609344 km/h, so divide: 100 ÷ 1.609344 = 62.13711922 mph.

60 mph to km/h. Multiply by the same figure: 60 × 1.609344 = 96.56064 km/h, an exact answer with no rounding.

20 knots to km/h and mph. A knot is 1.852 km/h, so 20 kn = 20 × 1.852 = 37.04 km/h. In miles per hour that is 23.01558896 mph, because a knot is about 1.150779448 mph.

100 km/h to m/s. 100,000 m in 3,600 s is 100 ÷ 3.6 = 27.77777778 m/s. A handy mental shortcut: divide km/h by 3.6 to get m/s, multiply m/s by 3.6 to get km/h.

Common speed conversions

Converting from miles per hour, knots or feet per second to metric units always gives an exact result. The rounding appears only in the other direction.

Mistakes to avoid

• A knot is already “per hour”. “Knots per hour” would be an acceleration; a boat doing 20 knots covers 20 nautical miles in an hour.
• Knots and mph are not interchangeable. A knot is about 15% faster than a mile per hour, so a wind of 30 kn is about 34.5 mph, not 30.
• Speed is not pace. Runners often think in minutes per mile or per kilometer, which is time divided by distance, the inverse of speed. The pace calculator handles that; to convert only the distance, use the length converter.
• Mach figures depend on the air. The same aircraft speed is a higher Mach number in cold air. Use the Mach unit here for a rough sea-level comparison only.
• Average speed over a trip is total distance divided by total time, not the average of the speeds you drove. For what a trip costs in fuel, see the fuel cost calculator.