Speed Unit Converter

A speed converter turns a value in one speed unit into another. This tool supports 12 common units: SI metric speeds - metre per second (m/s), kilometre per second (km/s), centimetre per second (cm/s), and millimetre per second (mm/s); transport speeds - kilometre per hour (km/h) and mile per hour (mph); aviation and marine speeds - the knot (one nautical mile per hour) and Mach number (about 340.29 m/s at the ISA sea-level reference); imperial speeds - foot per second (ft/s), inch per second (in/s), and yard per second (yd/s); plus the vacuum speed of light c (299 792 458 m/s) as the relativistic upper bound. Whether you are reading mph off a foreign dashboard, decoding a 'cruising at Mach 0.85' line in a flight report, turning ship speed from knots into km/h, or converting ballistic test data from ft/s to SI units, you can do it here in one step. All calculations run locally in your browser; nothing is uploaded.

Speed is the rate of change of position with respect to time, and its SI derived unit is the metre per second (m/s); km/s, cm/s, and mm/s are just decimal multiples of m/s with SI prefixes, not independent SI base units. After the 2019 SI redefinition the metre is fixed by the vacuum speed of light c = 299 792 458 m/s (exact), and the second by the caesium-133 ground-state hyperfine frequency Δν_Cs = 9 192 631 770 Hz (exact), so m/s is itself exact inside the SI. The converter stores every other unit as a fixed scalar multiple of m/s, and each conversion is a single floating-point multiplication value × (factor_from / factor_to). The core constants: 1 km/h = 1000/3600 m/s = 5/18 m/s (exact fraction); 1 mph is built on the international mile 1 mile = 1609.344 m exactly (1959 international yard-and-pound agreement), so 1 mph = 1609.344/3600 m/s = 0.447 04 m/s exactly; 1 ft/s = 0.304 8 m/s exactly (international foot); 1 knot = 1852/3600 m/s ≈ 0.514 444 m/s (international nautical mile 1 nm = 1852 m, set by the 1929 International Hydrographic Conference); 1 in/s = 0.025 4 m/s exactly; 1 yd/s = 0.914 4 m/s exactly. All of these imperial factors are rational numbers and introduce no floating-point error of their own - the only approximation happens at display time when results are rounded. Strictly speaking Mach is not an absolute speed unit but a dimensionless ratio - object speed divided by the local speed of sound. This tool uses the speed of sound in dry air at the ISA sea-level reference of 15 °C, a₀ = √(γRT) ≈ 340.29 m/s (adiabatic index γ = 1.4, dry-air specific gas constant R = 287.05 J/(kg·K), T = 288.15 K). In real flight the speed of sound scales with temperature: in the troposphere a = a₀ √(T/288.15), so at 11 km altitude with T = −56.5 °C the speed of sound drops to ≈ 295.07 m/s. A 'true Mach number' in supersonic flight has to be corrected against the local temperature reported by the air-data computer. So the Mach conversion here is fine for teaching and back-of-the-envelope work, but not a substitute for an exact aerospace calculation. The speed of light c = 299 792 458 m/s is an SI defining constant (17th CGPM, 1983) and carries no uncertainty. Newtonian mechanics adds velocities linearly, while relativity uses the Einstein velocity-addition formula v = (u + w)/(1 + uw/c²); at ordinary engineering speeds (v ≪ c) the two agree to many decimals - a jetliner at 270 m/s is only ≈ 9 × 10⁻⁷ c, and whether or not you apply the relativistic correction depends on whether your experiment is sensitive to relative deviations on the order of 10⁻¹². Numerical accuracy is bounded by IEEE 754 double precision (about 15-17 significant decimal digits, machine epsilon 2⁻⁵² ≈ 2.22 × 10⁻¹⁶). The widest span in this converter is c → mm/s, a ratio of about 3 × 10¹¹, still well inside the safe range of double precision, so chained multiplications and divisions never overflow or underflow. The display layer rounds to 6-9 significant figures, and the unit conversion itself loses essentially no precision.

• Metre per second definition: 1 m/s = 1 m / 1 s; the 2019 SI fixes c and Δν_Cs, making m/s exact inside the SI. km/s, cm/s and mm/s are SI-prefixed multiples of m/s, not independent base units.
• 1 km/h = 5/18 m/s (exact fraction), which is where the 'divide by 3.6' mental trick comes from; 1 mph = 0.447 04 m/s exactly, anchored to the international mile 1 mile = 1609.344 m.
• 1 knot = 1852/3600 m/s ≈ 0.514 444 m/s; the knot is one international nautical mile per hour, used for ships, aircraft, and meteorological wind speed.
• Mach is a dimensionless ratio; this tool references the ISA sea-level speed of sound 340.29 m/s, fine for teaching and rough estimates but not for precise aerospace work, which must correct for the local temperature.
• 1 ft/s = 0.304 8 m/s exactly; 1 yd/s = 0.914 4 m/s exactly; 1 in/s = 0.025 4 m/s exactly. The imperial speed units all convert through rational factors, so they introduce no floating-point approximation.
• The speed of light c = 299 792 458 m/s exactly is an SI defining constant (1983 CGPM); relativistic velocity addition v = (u+w)/(1+uw/c²) reduces to the Newtonian sum at ordinary engineering speeds.
• IEEE 754 double precision gives ~15-17 significant digits; the widest span here, c → mm/s, is about 3 × 10¹¹, far below the overflow limit, but display should still be rounded to 6-9 significant figures to avoid false precision.