Speed calculator,
solve for speed, distance, or time.

Field guide

Speed, distance, and time: the fundamental physics triangle.

The relationship between speed, distance, and time is one of the most fundamental equations in physics and everyday life. The formula is elegantly simple:

Speed = Distance ÷ Time  (s = d / t)

From this single equation, two rearrangements follow:

• Distance = Speed × Time  (d = s × t): how far you travel at a given speed over a given time.
• Time = Distance ÷ Speed  (t = d / s): how long it takes to cover a given distance at a given speed.

Speed vs. velocity

In everyday language, "speed" and "velocity" are often used interchangeably, but in physics they are distinct:

• Speed is a scalar quantity; it has magnitude only. A car travelling at 60 mph has a speed of 60 mph regardless of direction.
• Velocity is a vector quantity; it has both magnitude and direction. "60 mph north" is a velocity.

For the purposes of this calculator (computing travel times, road trip distances, running pace), speed (the scalar) is what you want. Velocity matters when direction is relevant, such as in navigation, ballistics, or orbital mechanics.

Average speed vs. instantaneous speed

The formula s = d/t gives average speed over the entire journey, not the instantaneous speed at any moment. Your car's speedometer shows instantaneous speed (the rate of change of position at a single moment). If you drive 120 miles in 2 hours, your average speed is 60 mph, even if you were briefly stopped at traffic lights and briefly drove 75 mph on the freeway.

Instantaneous speed is the calculus limit of average speed as the time interval approaches zero: v = lim(Δt→0) Δd/Δt = ds/dt.

Reference speeds: from walking to light

Speed varies by more than twelve orders of magnitude across natural phenomena. Here is a reference table of commonly referenced speeds:

Units of speed explained

• mph (miles per hour): the standard unit in the United States and United Kingdom for road speeds, aviation weather, and everyday use.
• km/h (kilometres per hour): used in most of the world for road signs, vehicle speedometers, and general use. 1 mph = 1.60934 km/h.
• m/s (metres per second): the SI base unit for speed. Used in physics, engineering, and scientific contexts. 1 m/s = 3.6 km/h = 2.237 mph.
• ft/s (feet per second): used in US engineering, ballistics, and some sports contexts. 1 ft/s = 0.6818 mph.
• knots (nautical miles per hour): the standard unit for maritime and aviation speed worldwide. 1 knot = 1.852 km/h = 1.151 mph. A nautical mile is defined as 1 minute of latitude arc (1.852 km).

Common speed calculation examples

Road trip planning

You need to drive 350 miles. At an average speed of 65 mph, how long will it take?

t = d / s = 350 miles / 65 mph ≈ 5.38 hours (5 hr 23 min)

Add 30 minutes for fuel and rest stops, and plan for a 6-hour trip.

Running pace and finish time

A marathon is 26.2 miles. If you run at 6.5 mph average, how long to finish?

t = 26.2 / 6.5 ≈ 4.03 hours (4 hr 2 min)

Note: runners often think in pace (minutes per mile) rather than mph. 6.5 mph = 60 / 6.5 ≈ 9.23 minutes per mile, or a 9:14/mile pace.

Astronomical distances

Light travels at 299,792,458 m/s (~186,282 miles per second). The Sun is ~93 million miles from Earth. How long does light take to travel from the Sun to Earth?

t = 93,000,000 miles / 186,282 miles per second ≈ 499 seconds (8 min 19 sec)

This is why astronomers say the Sun is "8 light-minutes" away.

The Mach number

The Mach number expresses speed as a multiple of the speed of sound. At sea level and 20°C, the speed of sound is approximately 343 m/s (767 mph). Mach 1 = the speed of sound, Mach 2 = twice the speed of sound, etc.

• Subsonic: below Mach 0.8 (most commercial aircraft cruise at Mach 0.78–0.85).
• Transonic: Mach 0.8–1.2, the region around the sound barrier where shockwaves begin to form.
• Supersonic: Mach 1.2–5.0; the Concorde cruised at Mach 2.02 (1,354 mph).
• Hypersonic: above Mach 5; the Space Shuttle reentered at approximately Mach 25.

The speed of sound varies with temperature and medium. It's faster in warmer air and much faster in water (~1,484 m/s) and steel (~5,960 m/s).

Physics of speed and kinetic energy

Speed has a non-linear relationship with kinetic energy:

KE = ½ × m × v²

Because speed is squared, doubling your speed quadruples your kinetic energy and therefore your braking distance. A car traveling at 60 mph has four times the kinetic energy of the same car at 30 mph, which is why highway crashes are so much more severe than low-speed fender benders.

This is also why aerodynamic drag matters at high speeds: drag force increases with v², so the power required to maintain speed grows with v³. Doubling your cycling speed requires roughly eight times the power.