Kinetic energy and momentum both describe a moving object but behave differently. Enter the mass and velocity to get both, and see how doubling the speed quadruples the energy.
Enter the mass in kg.
Enter the velocity in m/s.
Read the energy and momentum.
Kinetic energy: KE = ½ m v²
Momentum: p = m v
Every moving object carries kinetic energy and momentum. This calculator takes the mass in kilograms and the velocity in m/s and returns both: kinetic energy KE = ½mv² in joules and kilojoules, and momentum p = mv in kg·m/s. Seeing the two side by side is useful, because they grow with speed in very different ways.
Kinetic energy tells you how much work a moving object can do, or how much work is needed to stop it. Momentum tells you how hard it is to change its motion and is the quantity shared out in collisions. Road safety campaigns in India stress that speed kills, and the square of v in the energy formula is the physics behind that message. Class 9 and Class 11 students use both quantities in work-energy and collision problems.
1. Write the mass in kilograms.
2. Convert the velocity to m/s. For km/h, divide by 3.6.
3. Square the velocity, multiply by the mass and halve the result: KE = ½ × m × v². The answer is in joules.
4. Divide by 1000 to express the energy in kilojoules.
5. Multiply mass by velocity for momentum: p = m × v, in kg·m/s. Keep the sign of v, since momentum has a direction.
6. If you know momentum and mass, you can also get energy from KE = p² ÷ 2m.
Push an object from rest with a constant net force F over a distance s. The work done is W = Fs. Newton's second law gives F = ma, and the kinematics equation v² = 0 + 2as gives s = v² ÷ 2a. Multiplying, W = ma × v² ÷ 2a = ½mv². So kinetic energy is the work stored in the object by bringing it up to speed, and the same amount of work must be removed, usually by friction or a collision, to bring it back to rest.
Energy depends on v², so doubling speed makes the energy four times larger, while doubling mass only doubles it. A car at 80 km/h carries about 1.8 times the energy it has at 60 km/h. Since braking force is roughly fixed, the braking distance grows in the same proportion. Momentum, by contrast, is proportional to v, so the same doubling of speed only doubles the momentum. This difference is why energy governs damage and momentum governs the push in a collision.
Kinetic energy is a scalar and can never be negative, because v is squared. Momentum is a vector and its sign shows direction. In any collision with no outside forces, total momentum is conserved. Total kinetic energy is conserved only in elastic collisions, like ideal billiard balls; in real crashes some becomes heat, sound and deformation. Two identical cars meeting head-on at equal speeds have zero total momentum but a large total kinetic energy, all of which is lost in the crash.
Meera's 150 kg motorcycle, with her on it, is cruising at 25 m/s, which is 90 km/h, on the Mumbai–Pune Expressway.
Kinetic energy: KE = ½ m v² = 0.5 × 150 × 25² = 46,875 J
Momentum: p = m v = 150 × 25 = 3,750 kg·m/s
Answer: Kinetic energy 46,875 J; Momentum 3,750 kg·m/s
Entering speed in km/h instead of m/s, which inflates the energy by a factor of nearly 13.
Forgetting the ½ in the energy formula.
Squaring the mass instead of the velocity.
Assuming kinetic energy is conserved in every collision, when only momentum always is.
Adding momenta of objects moving in opposite directions without giving them opposite signs.
Solving work-energy and collision problems in Class 9, 11 and JEE.
Explaining in road safety lessons why a small increase in speed makes crashes much worse.
Estimating the energy a brake system must absorb and turn into heat.
Comparing the stopping power of a cricket ball and a football at match speeds.
Rough design checks for crash barriers and safety nets.
How do I convert km/h to m/s?
Divide by 3.6; 72 km/h = 20 m/s.
Can kinetic energy be negative?
No, because velocity is squared.