Velocity Calculator
Calculate velocity, speed, distance, or time using v = d/t. Includes unit conversions between m/s, km/h, and mph, plus worked examples for physics homework.
Velocity describes how fast an object is moving and in which direction. For introductory physics, speed and velocity are often used interchangeably — this calculator works for both.
Velocity Formula
v = d ÷ t (velocity = distance ÷ time)
d = v × t (distance = velocity × time)
t = d ÷ v (time = distance ÷ velocity)
Where:
- v = velocity (or speed) in m/s, km/h, or mph
- d = distance in metres, kilometres, or miles
- t = time in seconds, minutes, or hours
Examples:
- Car travels 120 km in 1.5 hours: v = 120 ÷ 1.5 = 80 km/h
- Train at 200 km/h for 2.5 hours: d = 200 × 2.5 = 500 km
- Sprint 100 metres at 10 m/s: t = 100 ÷ 10 = 10 seconds
Velocity vs Speed: The Distinction
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 north).
For most everyday calculations (and most physics homework problems), the distinction doesn't affect the formula. It matters when:
- An object changes direction (a runner on a circular track has changing velocity despite constant speed)
- You're calculating net displacement vs total distance
- You're working with vectors in 2D or 3D space
When Acceleration Is Known
If an object starts with initial velocity u and accelerates at rate a for time t:
v = u + at (final velocity)
d = ut + ½at² (distance covered)
v² = u² + 2ad (velocity without time)
Example — a car accelerates from 0 to 100 km/h in 6.5 seconds:
- Initial velocity: u = 0 m/s
- Final velocity: v = 100 km/h = 27.78 m/s
- Acceleration: a = (27.78 − 0) ÷ 6.5 = 4.27 m/s²
Example — same car, distance covered during acceleration:
d = 0 × 6.5 + ½ × 4.27 × 6.5² = 0 + 0.5 × 4.27 × 42.25 = 90.2 metres
Unit Conversions
| From | To m/s | To km/h | To mph |
|---|---|---|---|
| 1 m/s | — | × 3.6 | × 2.237 |
| 1 km/h | × 0.2778 | — | × 0.6214 |
| 1 mph | × 0.4470 | × 1.6093 | — |
| 1 ft/s | × 0.3048 | × 1.0973 | × 0.6818 |
Common speed reference points:
| Speed | m/s | km/h | mph |
|---|---|---|---|
| Walking (moderate) | 1.4 | 5.0 | 3.1 |
| Jogging | 2.8 | 10 | 6.2 |
| Cycling (moderate) | 5.6 | 20 | 12.4 |
| City speed limit (UK/EU) | 8.3 | 30 | 18.6 |
| Motorway speed limit (UK) | 31.3 | 112.6 | 70 |
| Highway speed limit (US) | 26.8 | 96.6 | 60 |
| Usain Bolt (100m world record) | 10.44 | 37.6 | 23.4 |
| Sound in air (20°C) | 343 | 1,235 | 767 |
| Light (in vacuum) | 299,792,458 | 1,079,252,848 | 670,616,629 |
Worked Examples for Physics Homework
Example 1 — Classic uniform velocity
A car travels at 60 km/h for 45 minutes. How far does it go?
t = 45 min = 0.75 hours
d = v × t = 60 × 0.75 = 45 km
Example 2 — Find velocity
A ball is thrown and travels 25 metres in 2 seconds. What is its speed?
v = d ÷ t = 25 ÷ 2 = 12.5 m/s
Example 3 — Find time
How long to travel 480 km at an average speed of 120 km/h?
t = d ÷ v = 480 ÷ 120 = 4 hours
Example 4 — With acceleration (kinematics)
A train starts from rest and reaches 72 km/h in 40 seconds. What is its acceleration and how far does it travel?
u = 0, v = 72 km/h = 20 m/s, t = 40 s
a = (v − u) ÷ t = (20 − 0) ÷ 40 = 0.5 m/s²
d = ut + ½at² = 0 + ½ × 0.5 × 1,600 = 400 m
Frequently Asked Questions
What is the difference between velocity and acceleration?
Velocity is how fast an object is moving (and in what direction). Acceleration is the rate at which velocity changes. A car going at constant 60 km/h has zero acceleration. A car braking from 60 to 0 has negative acceleration (deceleration). Formula: a = (v − u) ÷ t.
Can velocity be negative?
Yes. A negative velocity means the object is moving in the opposite direction to the defined positive direction. If "north" is positive, a velocity of −10 m/s means the object is moving south at 10 m/s. In 1D problems (like a car on a straight road), negative velocity typically means moving in reverse.
What is instantaneous velocity vs average velocity?
Average velocity = total displacement ÷ total time — it describes the overall motion. Instantaneous velocity = velocity at a specific instant, measured as the limit of displacement over an infinitely small time interval (calculus: v = ds/dt). Speedometers show instantaneous speed. The average for a trip is what you calculate with total distance and time.
Why is the speed of light the universal speed limit?
According to Special Relativity (Einstein, 1905), the speed of light (c ≈ 299,792,458 m/s) is constant in all reference frames. As an object approaches c, its relativistic mass increases, requiring infinite energy to reach c. Nothing with mass can reach the speed of light — only massless particles (photons) travel at c.
How does GPS calculate speed?
GPS devices measure speed by calculating the change in position over small time intervals. They compare satellite signal timing to triangulate position every 0.1–1 second, then calculate v = Δd ÷ Δt. Modern GPS units are accurate to ±0.1–0.5 m/s for speed. Accuracy degrades under tree cover, between buildings, or in tunnels.
Related Calculators
- Acceleration Calculator — calculate acceleration from velocity change
- Force Calculator — Newton's Second Law: F = ma
- Kinetic Energy Calculator — energy from mass and velocity
- Free Fall Calculator — velocity and distance under gravity