What is Velocity?
Velocity is the rate at which an object changes its position. It is one of the most fundamental quantities in physics, used to describe how fast something is moving and — for vector applications — in what direction. The average velocity (or speed) formula is:
v = d ÷ t
where v is velocity (speed), d is distance (or displacement), and t is time. This single equation can be rearranged to find any one of the three quantities when the other two are known.
Velocity appears in virtually every area of physics, from classical mechanics and fluid dynamics to relativity and quantum mechanics. In everyday life it governs how long a journey takes, how fast a download completes, and how quickly a chemical reaction proceeds.
The SI unit of velocity is metres per second (m/s). Depending on context, km/h is used for road travel, mph for aviation and road use in the USA and UK, knots for maritime and air navigation, and ft/s in some engineering applications.
Velocity is a vector quantity — it has both magnitude and direction. Speed is the scalar equivalent (magnitude only). For straight-line motion in a constant direction, the numerical values are equal and the terms are often used interchangeably.
v = d / t — Speed equals distance divided by time
| Variable | Symbol | SI Unit |
|---|
| Speed / Velocity | v | metres per second (m/s) |
| Distance / Displacement | d | metres (m) |
| Time | t | seconds (s) |
Rearrangements:
- Distance: d = v × t
- Time: t = d ÷ v
Unit conversion quick reference:
| From | To m/s | To km/h | To mph |
|---|
| 1 m/s | — | × 3.6 | × 2.2369 |
| 1 km/h | ÷ 3.6 | — | × 0.6214 |
| 1 mph | × 0.44704 | × 1.60934 | — |
| 1 ft/s | × 0.3048 | × 1.09728 | × 0.6818 |
How to Use
- Select a mode — choose Find Speed/Velocity, Find Distance, or Find Time depending on what you want to calculate.
- Enter the two known values — type the numbers you know and select the correct units from the dropdowns.
- Click Calculate — the unknown value is computed instantly.
- Read all unit conversions — all four speed units, all distance units, and all time units are displayed at once so you never need to convert manually.
- Check the formula — the formula section shows the exact equation used, useful for homework or exam preparation.
Example Calculations
Example 1 — Car journey:
A car travels 240 km in 3 hours. What is its average speed?
v = d ÷ t = 240 km ÷ 3 h = 80 km/h = 22.22 m/s = 49.71 mph = 72.93 ft/s
Example 2 — Sprint:
Usain Bolt ran 100 m in 9.58 seconds. What was his average speed?
v = 100 m ÷ 9.58 s = 10.438 m/s = 37.578 km/h = 23.350 mph = 34.245 ft/s
Example 3 — Flight distance:
An aircraft cruises at 900 km/h. How far does it travel in 8 hours?
d = v × t = 900 km/h × 8 h = 7,200 km = 7,200,000 m = 4,473.5 mi
Example 4 — Find time:
A train travels at 160 km/h. How long does it take to cover 400 km?
t = d ÷ v = 400 km ÷ 160 km/h = 2.5 hours = 150 minutes = 9,000 seconds
Example 5 — Speed of light comparison:
The speed of light is 299,792,458 m/s. In km/h: 299,792,458 × 3.6 = 1,079,252,848.8 km/h. In mph: 299,792,458 × 2.2369 = 670,616,629 mph.
Example 6 — Walking pace:
A person walks 5 km in 1 hour. Average speed = 5 km/h = 1.389 m/s = 3.107 mph = 4.572 ft/s. To walk 2 km at this pace: t = 2 ÷ 5 = 0.4 hours = 24 minutes.
What is the formula for velocity?
The basic formula for average velocity (or speed) is v = d ÷ t, where v is velocity, d is displacement (or distance), and t is time. Rearranging gives distance as d = v × t and time as t = d ÷ v. In SI units, velocity is measured in metres per second (m/s), distance in metres (m), and time in seconds (s). This relationship is one of the most fundamental in all of physics.
What is the difference between velocity and speed?
Speed is a scalar quantity — it has magnitude only (e.g. 60 km/h). Velocity is a vector quantity — it has both magnitude and direction (e.g. 60 km/h due north). For straight-line motion in one direction, speed and the magnitude of velocity are equal. When direction changes, average speed (total path length ÷ time) can differ from average velocity magnitude (displacement ÷ time).
How do I convert km/h to m/s?
To convert km/h to m/s, divide by 3.6. For example, 100 km/h ÷ 3.6 = 27.78 m/s. The factor 3.6 comes from the fact that 1 km = 1000 m and 1 hour = 3600 s, so 1 km/h = 1000/3600 m/s = 1/3.6 m/s. To go the other way (m/s to km/h), multiply by 3.6.
How do I convert mph to m/s?
1 mph = 0.44704 m/s exactly (by definition). To convert mph to m/s, multiply by 0.44704. For example, 60 mph × 0.44704 = 26.82 m/s. To convert m/s to mph, divide by 0.44704 (or multiply by 2.237). A quick mental shortcut: 1 m/s ≈ 2.237 mph, so 10 m/s ≈ 22.4 mph.
What is the SI unit of velocity?
The SI unit of velocity is metres per second (m/s or m·s⁻¹). Other common units include kilometres per hour (km/h), miles per hour (mph), feet per second (ft/s), and knots (1 knot = 1 nautical mile per hour ≈ 0.5144 m/s). In scientific contexts m/s is standard; km/h and mph are used in everyday transportation.
What is average velocity vs instantaneous velocity?
Average velocity is total displacement divided by total time over an entire journey: v_avg = Δd/Δt. Instantaneous velocity is the velocity at a specific instant — it is the limit of average velocity as the time interval approaches zero, which in calculus equals the derivative of position with respect to time: v = dx/dt. A car's speedometer shows instantaneous speed; average speed is what you calculate after a trip.
How does acceleration relate to velocity?
Acceleration (a) is the rate of change of velocity over time: a = (v_final - v_initial) / t. If an object starts at rest and reaches 20 m/s in 4 seconds, its average acceleration is 5 m/s². You can rearrange to find final velocity: v = u + at, where u is initial velocity. The full set of kinematic equations also relates displacement, velocity, acceleration, and time for uniform acceleration.
If a car travels 120 km in 1.5 hours, what is its average speed?
Average speed = distance ÷ time = 120 km ÷ 1.5 h = 80 km/h. Converting to m/s: 80 ÷ 3.6 = 22.22 m/s. Converting to mph: 80 ÷ 1.609 = 49.71 mph. Using our calculator, enter distance = 120, unit = km, time = 1.5, unit = hr and click Calculate to get all conversions at once.
What is the speed of light and sound?
The speed of light in a vacuum is exactly 299,792,458 m/s (approximately 3 × 10⁸ m/s or 1,079,252,848.8 km/h). The speed of sound in dry air at 20°C is approximately 343 m/s (1,235 km/h or 767 mph). A Mach number expresses speed as a multiple of the local speed of sound; Mach 1 = the speed of sound at that altitude and temperature.
How do I calculate how long it takes to drive somewhere?
Use t = d ÷ v. For example, a 240 km trip at 80 km/h takes 240 ÷ 80 = 3 hours. In our calculator, select Find Time mode, enter your speed and distance, and the result appears in seconds, minutes, and hours. Remember this gives driving time only; add buffer for traffic, stops, and variable speeds.
What is terminal velocity?
Terminal velocity is the maximum speed a falling object reaches when air resistance equals the gravitational force, so net force and therefore acceleration become zero. For a skydiver in a stable horizontal position, terminal velocity is approximately 55 m/s (200 km/h). Terminal velocity depends on the object's mass, cross-sectional area, drag coefficient, and air density. A denser or more streamlined object has higher terminal velocity.
Can velocity be negative?
Yes. Because velocity is a vector, a negative value simply means motion in the opposite direction to your chosen positive reference. If you define rightward as positive, then a leftward velocity of 5 m/s is −5 m/s. Speed (the magnitude of velocity) is always non-negative. This sign convention is essential when applying kinematic equations to problems with changing direction.
What is the difference between displacement and distance?
Distance is the total path length travelled, regardless of direction. Displacement is the straight-line vector from start to end point. If you walk 4 m east then 3 m north, your distance is 7 m but your displacement magnitude is √(4² + 3²) = 5 m. For average speed, divide total distance by time. For average velocity, divide displacement by time. In straight-line motion without direction reversal, they are equal.