Velocity Calculator
Calculate speed, velocity, and kinematics with unit conversions
Calculate velocity: v = d / t
Velocity, Speed, and How to Calculate Them
Velocity is the rate of change of position — distance traveled per unit of time, with a direction. In everyday use the basic formula is v = d / t: a cyclist covering 30 km in 1.5 hours averages 30 / 1.5 = 20 km/h. Strictly, speed is the magnitude only, while velocity includes direction; that distinction matters in the Relative tab, where direction determines whether speeds add or subtract.
Kinematic Equations for Constant Acceleration
The Kinematics tab solves the standard equations of uniformly accelerated motion:
- v = v₀ + at — final velocity from initial velocity, acceleration, and time.
- v² = v₀² + 2ad — final velocity when you know distance instead of time.
Example: a ball dropped from rest accelerates at g = 9.81 m/s². After 3 seconds it is falling at v = 0 + 9.81 × 3 = 29.4 m/s, which is about 106 km/h.
Speed Unit Conversions
The Convert tab translates between common speed units. Key conversion factors: 1 m/s = 3.6 km/h = 2.237 mph = 1.944 knots. So 100 km/h is 27.78 m/s or 62.14 mph, and a 20-knot wind is 10.29 m/s (37 km/h). Mach 1, the speed of sound at sea level and 15 °C, is about 343 m/s (1,235 km/h), though it varies with air temperature.
Relative Velocity
When two objects move along the same line, their relative velocity is the difference of their velocities if they travel in the same direction, and the sum if they approach head-on. Two trains approaching each other at 80 km/h and 100 km/h close the gap at 180 km/h; if the faster one is overtaking the slower in the same direction, it gains only 20 km/h.
Typical Speeds for Reference
- Brisk walking: about 1.4 m/s (5 km/h)
- Usain Bolt's peak sprint: about 12.4 m/s (44.7 km/h)
- Highway driving: 27.8 m/s (100 km/h)
- Commercial jet cruise: about 250 m/s (900 km/h, Mach 0.85)
- Earth orbiting the Sun: about 29,780 m/s
Frequently Asked Questions
How do I calculate velocity from distance and time?+
Divide distance by time: v = d / t. If you run 5 km in 25 minutes, that is 5,000 m ÷ 1,500 s = 3.33 m/s, or 12 km/h. The Basic tab lets you mix units — meters, kilometers, miles, feet with seconds, minutes, or hours — and can also solve for distance or time instead.
What is the difference between speed and velocity?+
Speed is how fast something moves; velocity is how fast and in what direction. Two cars doing 60 km/h in opposite directions have the same speed but different velocities. The distinction matters in the Relative tab, where opposite directions make speeds add (closing speed) and same directions make them subtract.
How do I convert km/h to mph or m/s?+
Use the Convert tab: enter a value and its unit, and the calculator shows it in m/s, km/h, mph, ft/s, and knots simultaneously. The key factors are 1 m/s = 3.6 km/h and 1 mph = 1.609 km/h, so 100 km/h equals 62.14 mph and 27.78 m/s.
Can this calculator solve kinematics problems with acceleration?+
Yes. The Kinematics tab handles constant-acceleration motion using v = v₀ + at and v² = v₀² + 2ad, and can solve for final velocity, initial velocity, acceleration, or time depending on which values you know. It is designed for typical physics homework problems like free fall and braking distance.
Is the velocity calculator free and does it work on my phone?+
Yes. It is completely free with no sign-up, and every calculation runs locally in your browser — nothing is sent to a server. The responsive design works on phones, tablets, and desktops.
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