Velocity Calculator: Average, Final, Angular and Escape Velocity
Calculate average velocity, final or initial velocity under constant acceleration, angular velocity and escape velocity, with step-by-step working. Enter distance in metres, kilometres, miles or feet and get the answer in m/s, km/h, mph and ft/s. 100% private — runs in your browser.
A velocity calculator works out how fast the position of an object changes, and in which direction. This one covers five cases: average velocity from displacement and time (v = d/t), final or initial velocity under constant acceleration (v = u + at), angular velocity (ω = θ/t) with linear speed v = ωr, and escape velocity (v = √(2GM/r)).
Velocity Calculator Formulas with Worked Examples
Each row below was calculated with the tool above. Pick the mode and press Load Example to reproduce the first example for that mode.
| Mode | Formula | Example input | Result |
|---|---|---|---|
| Average velocity | v = d ÷ t | 150 m in 12 s | 12.5 m/s (45 km/h, 27.96 mph) |
| Average velocity, other units | v = d ÷ t | 60 mi in 1.5 h | 17.8816 m/s (40 mph, 64.37 km/h) |
| Final velocity | v = u + at | u = 5 m/s, a = 2 m/s², t = 8 s | 21 m/s (75.6 km/h) |
| Initial velocity | u = v − at | v = 30 m/s, a = 3 m/s², t = 6 s | 12 m/s (43.2 km/h) |
| Angular velocity | ω = θ ÷ t | 360° in 2 s | 3.1416 rad/s (180 °/s, 30 RPM) |
| Linear speed from rotation | v = ωr | ω = 3.1416 rad/s, r = 0.5 m | 1.5708 m/s |
| Escape velocity | v = √(2GM ÷ r) | Earth: M = 5.9722 × 1024 kg, r = 6.371 × 106 m | 11,186 m/s (11.186 km/s) |
How Velocity Calculations Work
Velocity is a fundamental concept in physics that describes how fast an object moves and in which direction. Unlike speed, which is a scalar quantity, velocity is a vector — it has both magnitude and direction. The simplest velocity formula is v = d/t, where v is velocity, d is displacement, and t is time. This gives you the average velocity over a time interval.
When an object accelerates uniformly, the kinematic equation v = u + at relates final velocity (v) to initial velocity (u), acceleration (a), and time (t). It is one of the constant-acceleration (SUVAT) equations used throughout classical mechanics. Rearranged, it gives the initial velocity when the final velocity and acceleration are known: u = v − at. For free fall near the Earth’s surface, the standard acceleration of gravity is 9.80665 m/s² (NIST Special Publication 811, Appendix B.9).
Units and Conversion Factors
The calculator converts every input to SI units (metres, seconds, radians) before applying the formula, then reports the result in several units. The factors are the exact definitions listed in NIST Special Publication 811, Appendix B.9.
| Quantity | Conversion used |
|---|---|
| Distance | 1 km = 1,000 m · 1 mi = 1,609.344 m · 1 ft = 0.3048 m |
| Time | 1 min = 60 s · 1 h = 3,600 s |
| Linear velocity | 1 m/s = 3.6 km/h · 1 mph = 0.44704 m/s · 1 ft/s = 0.3048 m/s |
| Angle | 360° = 2π rad = 1 revolution |
| Angular velocity | 1 RPM = 2π ÷ 60 rad/s = 0.1047198 rad/s |
Types of Velocity in Physics
Physics recognizes several types of velocity depending on the context. Average velocity is the total displacement divided by total time — useful for everyday calculations like travel speed. Instantaneous velocity is the velocity at a specific moment, found using calculus as the derivative of position with respect to time.
Angular velocity measures how fast an object rotates, expressed in radians per second. It is calculated as the angle swept divided by the time taken, and a point at distance r from the axis moves with linear speed v = ωr. Terminal velocity is the constant speed a falling object reaches when air resistance balances its weight. Escape velocity is the minimum speed needed for an object to break free from a planet’s gravitational pull without further propulsion.
Escape Velocity: Constants and Planet Values
Escape velocity is v = √(2GM/r), where G is the Newtonian constant of gravitation, 6.67430 × 10−11 m3 kg−1 s−2 (NIST, 2022 CODATA value), M is the mass of the body and r is the distance from its centre. The presets in the calculator use the mass and radius published in the NASA planetary fact sheets, and the results agree with the escape velocities NASA lists:
| Body | Mass (kg) | Radius (m) | Calculator result | NASA fact sheet |
|---|---|---|---|---|
| Earth | 5.9722 × 1024 | 6.371 × 106 | 11.186 km/s | 11.186 km/s |
| Moon | 7.346 × 1022 | 1.7374 × 106 | 2.376 km/s | 2.38 km/s |
| Mars | 6.4169 × 1023 | 3.3895 × 106 | 5.027 km/s | 5.03 km/s |
| Jupiter | 1.89813 × 1027 | 7.1492 × 107 | 59.532 km/s | 59.5 km/s |
Radii are the volumetric mean radius, except Jupiter, where the equatorial radius at the 1 bar pressure level is used. The formula ignores air resistance and the rotation of the body.
Velocity vs Speed — What is the Difference?
Speed and velocity are often confused, but they differ in a key way. Speed is a scalar quantity — it only tells you how fast something is moving. Velocity is a vector quantity — it tells you both the rate of motion and the direction. For example, a car traveling at 60 km/h has a speed of 60 km/h regardless of direction. But if it moves 60 km/h north and then 60 km/h south back to the start, its average velocity is zero because the net displacement is zero.
This distinction matters in physics calculations. When solving projectile motion, orbital mechanics, or collision problems, direction is essential. Velocity can be negative (indicating motion in the opposite direction), while speed is always positive or zero.
Real-World Velocity Applications
Velocity calculations are used everywhere in science and engineering. Automotive engineers use kinematic equations to model braking distances and acceleration profiles. Aerospace engineers use escape velocity when planning missions that leave Earth’s gravity. Sports scientists measure angular velocity to analyze a pitcher’s throwing motion or a gymnast’s spin rate. Navigation systems use velocity vectors to plot flight paths and ship routes. Even video game physics engines rely on velocity formulas for realistic motion simulation.
Last updated: October 2026. Constants checked against NIST and NASA sources in October 2026.
Frequently Asked Questions
What is the difference between speed and velocity?
Speed is a scalar quantity that only measures how fast something moves. Velocity is a vector that includes both magnitude and direction. An object can have constant speed but changing velocity if it changes direction.
What formula is used for average velocity?
Average velocity is calculated using v = d/t, where d is the total displacement (change in position) and t is the total time elapsed. Unlike average speed, average velocity considers direction. Example: a displacement of 150 m in 12 s gives 12.5 m/s.
How do you calculate final velocity with acceleration?
Use the kinematic equation v = u + at, where u is initial velocity, a is acceleration, and t is time. It holds for constant (uniform) acceleration, such as free fall near the surface of the Earth when air resistance is ignored. Example: u = 5 m/s, a = 2 m/s² and t = 8 s give v = 21 m/s.
What is angular velocity?
Angular velocity (ω) measures how fast an object rotates. It equals the angle swept in radians divided by time: ω = θ/t. One full rotation (360°) equals 2π radians, so one turn every 2 seconds is 3.1416 rad/s, or 30 RPM. It is commonly measured in rad/s or RPM.
What is escape velocity?
Escape velocity is the minimum speed needed to leave the gravitational field of a planet or moon without further propulsion, ignoring air resistance. The formula is v = √(2GM/r), where G is the gravitational constant, M the mass of the body and r its radius. For Earth it is about 11,186 m/s (11.2 km/s).
Can velocity be negative?
Yes, velocity can be negative. A negative velocity means the object is moving in the opposite direction relative to the chosen positive direction. For example, if upward is positive, a falling object has negative velocity.
How do you convert angular velocity to linear velocity?
Multiply the angular velocity in radians per second by the radius: v = ωr. A point 0.5 m from the axis of a wheel turning at 30 RPM (3.1416 rad/s) moves at about 1.571 m/s. Convert RPM to rad/s first by multiplying by 2π/60, which is about 0.10472.
How do I convert m/s to km/h and mph?
Multiply metres per second by 3.6 to get km/h, and divide by 0.44704 (multiply by about 2.23694) to get mph. The factors follow from the exact definitions of the kilometre, the hour and the international mile (1,609.344 m). For example, 12.5 m/s is 45 km/h, or about 27.96 mph.