Linear speed is how fast an object moves along a path, measured as the distance it covers divided by the time it takes. If a car travels 100 kilometers in 2 hours, its linear speed is 50 km/h. The formula is simple: speed equals distance divided by time (v = s/t). This is one of the most fundamental concepts in physics, and it shows up everywhere from classroom problems to sports performance tracking.
The Basic Formula
Linear speed is calculated by dividing the distance an object travels by the elapsed time. Written out, that’s v = s/t, where v is speed, s is distance, and t is time. The result is always expressed in distance units per time unit: meters per second, miles per hour, kilometers per day, or any combination that fits the situation.
The standard SI unit is meters per second (m/s). Other common conversions worth knowing:
- 1 mile per hour = 0.447 m/s
- 1 kilometer per hour = 0.278 m/s
- 1 knot (used in aviation and sailing) = 0.514 m/s
- 1 foot per second = 0.305 m/s
You pick whichever unit makes sense for the scale of what you’re measuring. A sprinter’s speed works well in m/s. A planet’s orbital speed makes more sense in thousands of kilometers per day.
Linear Speed vs. Angular Speed
Linear speed and angular speed describe the same motion from two different perspectives. Angular speed tells you how quickly something rotates, measured in radians per second or revolutions per minute. Linear speed tells you how far a point on that rotating object actually travels through space in a given time.
The connection between them depends entirely on radius. A point farther from the center of rotation covers more distance per revolution, so it has a higher linear speed even though the angular speed is identical. Think of a merry-go-round: a horse near the outer edge moves much faster through space than one near the center, even though both complete one full rotation in the same time. The relationship is v = 2πr/T, where r is the radius and T is the period (the time for one full rotation).
Calculating Linear Speed in Circular Motion
When an object moves in a circle, you can find its linear speed if you know the radius and how long one full rotation takes. The circumference of the circle (2πr) gives you the distance per rotation, and dividing by the period gives you speed.
Here’s a straightforward example: a car drives around a roundabout with a radius of 15 meters, completing one loop in 30 seconds. Plug those into the formula: v = 2π(15)/30 = π ≈ 3.14 m/s. The car’s linear speed is about 3.14 meters per second, or roughly 11.3 km/h.
The same formula works at planetary scales. Earth orbits the sun at a radius of roughly 91.5 million kilometers, completing one loop per year (365 days). That gives a linear speed of about 1.57 million kilometers per day, or around 107,000 km/h. You’re moving that fast right now, even sitting still.
Linear Speed in Human Performance
Linear speed is a central measurement in sports science, particularly in sprinting. The fastest linear speed ever recorded by a human belongs to Usain Bolt, who reached a peak of 12.32 m/s (about 27.6 mph) at roughly the 52-meter mark of his 100-meter world record. His average speed across the full race was 10.44 m/s. The gap between average and peak speed highlights an important distinction: a sprinter accelerates, hits top speed, then gradually decelerates before the finish line.
In team sports like soccer, linear speed (straight-line sprinting) is treated as a distinct physical quality from agility or change-of-direction speed. Research on young soccer players found strong correlations between 30-meter sprint times and agility test results (r = 0.744), but the abilities aren’t interchangeable. A player who’s fast in a straight line isn’t necessarily fast when cutting at sharp angles, which is why coaches measure both separately.
How Linear Speed Is Measured
The simplest way to measure linear speed is the stopwatch method: mark a known distance, time the crossing, divide. In professional and research settings, the tools are more precise. Timing gates use infrared beams placed at set intervals along a track. When an athlete breaks the beam, the system logs the exact time, and speed is calculated from the known distance between gates.
Research comparing different timing gate setups found that gates placed every 5 meters gave results nearly identical to radar gun measurements (correlation above 0.926), with a coefficient of variation under 1.7%. Gates placed every 10 meters were slightly less accurate, occasionally overestimating maximum sprint speed. For the most reliable results without expensive radar equipment, 5-meter splits are the current recommendation in sports science, with measurement precision small enough to detect speed differences under 0.02 m/s.
GPS units worn by athletes can also estimate linear speed in real time during games and training, though they’re generally less precise over very short distances than fixed timing systems.
Why “Linear” Matters
The word “linear” distinguishes this measurement from rotational or angular quantities. When you say a wheel spins at 300 revolutions per minute, that’s angular speed. When you say the edge of that wheel moves at 15 m/s, that’s linear speed. Both describe the same wheel, but linear speed captures what you’d actually feel if you were riding on the rim: the real distance covered through space. Any time you see a speedometer in a car, you’re reading linear speed, even though the wheels are rotating. The speedometer converts the wheel’s angular motion into the straight-line distance the car covers per hour.