Kinetic Energy Calculator finds KE from mass and velocity, solves for velocity or mass, works out the energy change between two speeds, and gives momentum and an equal drop height.
Enter the mass of the object and how fast it is moving.
Result Unit
Energy Curve
Energy rises with the square of velocity, so the curve steepens. Both axes rescale to fit your values.
Step-by-Step Working
- Formula: KE = ½ × m × v²
- Square the velocity: (5 m/s)² = 25 m²/s²
- Multiply: KE = ½ × 10 kg × 25 m²/s² = 125 J
Energy by Velocity
| Velocity (m/s) | Energy (J) | Momentum (kg·m/s) |
|---|---|---|
| 1.25 | 7.813 | 12.5 |
| 2.5 | 31.25 | 25 |
| 3.75 | 70.31 | 37.5 |
| 5 | 125 | 50 |
| 7.5 | 281.3 | 75 |
| 10 | 500 | 100 |
| 15 | 1,125 | 150 |
Kinetic Energy Calculator Modes and Units
The Kinetic Energy Calculator finds the energy an object has because it is moving. Enter a mass and a velocity and it returns the kinetic energy, along with the momentum, the drop height that would give the same speed, and how the energy changes at other speeds.
The Calculate menu has four modes. Kinetic Energy (KE) is the usual one. Velocity from KE and Mass and Mass from KE and Velocity solve the formula backward. Change in KE, v₁ to v₂ gives the energy needed to speed an object up, or removed to slow it down, between two speeds.
Mass can be typed in kilograms, grams, metric tons, pounds, ounces or grains. Velocity can be in m/s, km/h, km/s, mph, ft/s or knots. Results come out in joules by default, and the options switch them to kilojoules, megajoules, foot-pounds, kilocalories, watt-hours or electronvolts.
The default object is 10 kg moving at 5 m/s. The Kinetic Energy Calculator shows 125 J in motion, a momentum of 50 kg·m/s and an equal drop height of 1.275 m.
Kinetic Energy Formula
OpenStax University Physics defines the kinetic energy of a particle as one half the product of its mass and the square of its speed. Written as a formula, it is the kinetic energy equation every calculator uses.
$$KE = \frac{1}{2} m v^2$$
With m in kilograms and v in meters per second, KE is in joules. To calculate kinetic energy by hand, square the velocity, multiply by the mass and divide by 2. For the default object, 5² is 25, times 10 kg is 250, and half of that is 125 J.
The same source gives a worked case. An 80 kg athlete running at 10 m/s has ½ × 80 × 10² = 4,000 J, or 4.0 kJ. The step list in the Kinetic Energy Calculator prints these same lines with your own numbers, including any unit conversion it had to make first.
What is the 1/2 in the kinetic energy formula?
The one half comes from how the energy builds up. Kinetic energy equals the work a force does to bring an object from rest to its speed. Under a steady force, the speed rises evenly from zero, so the average speed during the push is half the final speed.
Work is force times distance, and the distance covered is the average speed times the time. Putting those together gives ½mv². It is the same one half that appears in the area of a triangle, which is why a graph of momentum against velocity has an area equal to the kinetic energy.
Kinetic Energy Calculator With Steps for Velocity and Mass
Turning the formula around gives the two other variables. The velocity mode uses the first form, and the mass mode uses the second. Both take the energy in joules and the other value in SI units before solving.
$$v = \sqrt{\frac{2 KE}{m}}$$
$$m = \frac{2 KE}{v^2}$$
A 10 kg object carrying 320 J moves at √(2 × 320 ÷ 10) = 8 m/s. An object with 320 J at 4 m/s has a mass of 2 × 320 ÷ 16 = 40 kg. In both modes the step list shows each line of the rearranged formula, so the working can be copied into homework or a report.
The fourth result card switches to the solved value in these modes. The velocity mode’s 8 m/s also reads as 28.8 km/h, 17.9 mph and 26.25 ft/s. The mass mode loads with 320 J at 5 m/s, which needs 25.6 kg, shown again as 56.44 lb, 25,600 g and 395,100 grains.
Kinetic energy can also be written with momentum, p = mv, as KE = p² ÷ 2m. The first result card gives the momentum next to the energy, along with the energy per kilogram, v² ÷ 2, which depends on speed alone.
Speed Counts More Than Mass
Velocity is squared in the formula and mass is not. Doubling the mass of the default object doubles its energy to 250 J, but doubling its speed quadruples the energy to 500 J. The third result card shows the double-speed and half-speed figures for any entry.
The effect is easiest to see with a car. A 1,500 kg car at 50 km/h has 144.7 kJ of kinetic energy, and at 100 km/h it has 578.7 kJ. The Change in KE mode of the Kinetic Energy Calculator shows that going from 50 to 100 km/h adds 434 kJ, three times the energy needed to reach 50 km/h from rest.
That gap is why braking distance and crash energy rise so steeply with speed, which the Stopping Distance Calculator shows on the road. The brakes have to remove all of that energy as heat. By the work-energy theorem, the net work done on an object equals its change in kinetic energy, and the result alert in Change in KE mode states that link for your numbers.
Kinetic and Potential Energy
Kinetic energy is energy of motion, and potential energy is stored energy of position. The formula for gravitational potential energy near the ground is PE = mgh, with g = 9.80665 m/s². The two trade places whenever something rises or falls.
$$m g h = \frac{1}{2} m v^2$$
The mass cancels, so the height that gives a speed depends on the speed alone, h = v² ÷ 2g. The second result card shows this equal drop height. For the default 5 m/s it is 1.275 m, reached after a fall of 0.51 s with no air resistance.
To calculate KE and PE together for a falling object, take its potential energy at the top as the kinetic energy at the bottom. A potential energy calculator handles the stored side directly, and the Impact Energy Calculator takes the falling object on into the collision.
Kinetic Energy Unit
The SI unit of kinetic energy is the joule. One joule is one kilogram times one meter squared per second squared, 1 kg·m²/s², which is the same as one newton acting over one meter.
Other fields use other units for the same quantity. The factors below come from NIST Special Publication 811, and the fourth result card lists the energy in three of them at once.
| Unit | Equals | Where it is used |
|---|---|---|
| 1 foot-pound (ft·lbf) | 1.355818 J | US ballistics, archery and engineering |
| 1 kilocalorie (kcal) | 4,184 J | Food energy and thermochemistry |
| 1 watt-hour (Wh) | 3,600 J | Batteries and flywheel storage |
| 1 electronvolt (eV) | 1.602177 × 10⁻¹⁹ J | Particle and atomic physics |
The default 125 J is 92.2 ft·lbf, 0.0299 kcal or 0.0347 Wh. The small kilocalorie figure shows why everyday motion is a tiny amount of energy next to food or fuel.
Kinetic Energy of Bullets and Arrows
The mass menu includes grains and the velocity menu includes feet per second, so the Kinetic Energy Calculator also works as a kinetic energy calculator for bullets and arrows. Set the result unit to foot-pounds to match ammunition boxes and archery charts.
A 400 grain arrow at 280 ft/s carries 69.65 ft·lbf, which is 94.4 J. For arrow speed from a bow’s rating, the Arrow Speed Calculator gives the velocity first. For firearms, the Bullet Energy Calculator adds the energy left at range, and the FPE Calculator covers airgun pellets against legal power limits.
Relativistic Kinetic Energy
The formula ½mv² holds only well below the speed of light. Near light speed, OpenStax University Physics Volume 3 gives the relativistic kinetic energy instead, where γ is the Lorentz factor.
$$K_{rel} = (\gamma – 1) m c^2$$
At everyday speeds the two agree. At 1 percent of light speed, the classical formula is low by only 0.0075 percent. At 10 percent it is low by 0.76 percent, and at half the speed of light it is low by 24 percent.
The Kinetic Energy Calculator warns you once a speed passes 1 percent of light speed, about 3,000 km/s. The alert gives the size of the error and the relativistic kinetic energy for your mass and speed. A speed at or above 299,792,458 m/s is rejected, since nothing with mass can reach it.
Kinetic Energy Examples
Anything that moves has kinetic energy. A 70 kg person walking at 1.4 m/s has 68.6 J. A 145 g baseball thrown at 90 mph has 117 J. A 1,500 kg car at 100 km/h has about 579 kJ, and wind, flowing water and spinning machinery all carry it too.
The object with the greatest kinetic energy is not always the heaviest or the fastest. It is the one with the largest product of mass and speed squared. OpenStax gives the extreme case of the Chicxulub asteroid, estimated at 1.7 × 10¹⁵ kg moving at 22 km/s, which released about 4.2 × 10²³ J on impact.
How is kinetic energy used in real life?
Enter any of these in the Kinetic Energy Calculator to compare them. Wind turbines and hydroelectric plants take kinetic energy from moving air and water and turn it into electricity. Hammers, pile drivers and crushers use the kinetic energy of a moving mass to do work in an instant.
Kinetic energy can also be stored. A flywheel keeps energy in its spin and gives it back on demand, and regenerative braking in electric cars turns some of the car’s kinetic energy into stored charge instead of heat.
What stops kinetic energy?
Kinetic energy is lost when a force acts against the motion. Friction, air drag and brakes do negative work, and that work turns the kinetic energy into heat, sound and deformation. Energy is not destroyed, only moved into other forms.
To lose kinetic energy, an object has to slow down. To increase kinetic energy, a net force has to push it faster, and the energy gained equals the work that force does. Halving a speed leaves only a quarter of the energy, which the third result card shows for your numbers.
Why is it called kinetic energy?
The name comes from the Greek word for motion, which also gives us kinematics and cinema. Kinetic energy is simply the energy an object has because it moves, and it falls to zero when the object is at rest in the frame you measure from.
That last point matters. OpenStax shows a 75 kg person walking at 1.5 m/s on a subway car has 84.4 J relative to the car, but several kilojoules relative to the tracks. Always enter the speed relative to whatever the object is about to hit or interact with.
Types of Kinetic Energy
Lists of five or seven types of kinetic energy mix true kinetic energy with forms that contain it. In physics, motion comes in three basic forms, and the others are built from them at a smaller scale.
Translational kinetic energy is motion from place to place, ½mv², which the Kinetic Energy Calculator handles. Rotational kinetic energy is spin, ½Iω², where I is the moment of inertia and ω the angular speed. Vibrational kinetic energy is motion back and forth about a fixed point.
Thermal energy is the random kinetic energy of atoms and molecules, which rises with temperature. Sound is a traveling vibration of particles, so it carries kinetic energy that trades back and forth with potential energy as the wave passes. That is why sound needs a medium and cannot travel through the vacuum of space.
Electrical energy in a wire and radiant energy in light are often listed too. They are forms of energy, but not kinetic energy of a mass in the sense of ½mv². For a spring or a stretched band, the Elastic Potential Energy Calculator covers the stored energy that turns into kinetic energy on release.