Kinetic & Potential Energy Calculator
Work out kinetic energy (½mv²) and gravitational potential energy (mgh), or solve for the speed, mass or height. Convert between the two, and between joules, kilojoules, kilocalories and kilowatt-hours.
How to Use
- Pick what to find: kinetic energy, speed or mass from ½mv²; potential energy, height or mass from mgh; or the speed after a fall and the height a throw can reach.
- Enter the known values with their units: kg, g, tonnes or pounds; m/s, km/h or mph; metres or feet; joules, kJ, kcal or kWh.
- For potential energy, keep g at 9.80665 m/s² for Earth or change it for another planet.
- Read the answer, the energy in a second unit and the matching drop height or landing speed; change any unit to convert.
- Follow the energy bars from top to ground, and see Show Work for each step and the full table of energy units.
Worked Example
A 1,500 kg car at 100 km/h. Convert the speed first: 100 ÷ 3.6 = 27.78 m/s. KE = ½ × 1,500 × 27.78² = 578,704 J (578.7 kJ, or 138.3 kcal). To gain that much energy by falling, the car would have to drop h = v² ÷ 2g = 39.3 m.
A 0.5 kg ball dropped from 20 m. PE = mgh = 0.5 × 9.80665 × 20 = 98.07 J. All of it becomes kinetic energy at the ground, so ½mv² = mgh and v = √(2gh) = √392.27 = 19.8 m/s, whatever the mass.
The common mistake: putting km/h straight into ½mv². ½ × 1,500 × 100² = 7,500,000 J, nearly 13 times too much (3.6² = 12.96). Convert to metres per second first: the right answer is 578.7 kJ.
Show Work
Formulas
Vis Viva to the Joule
In 1686 Gottfried Wilhelm Leibniz argued that the true measure of a body’s “living force”, vis viva, was mv², not the momentum mv favoured by Descartes’ followers. Willem ’s Gravesande dropped brass balls into soft clay and found that a ball hitting twice as fast made a dent four times as deep, and Émilie du Châtelet set out the case for mv² in her Institutions de physique of 1740.
The factor ½ arrived in 1829, when Gaspard-Gustave Coriolis defined work as force times distance and showed that the work done on a body equals ½mv². William Rankine introduced the term “potential energy” in 1853. In the 1840s James Prescott Joule showed with falling weights that turned a paddle wheel in water that mechanical energy always yields the same amount of heat; the SI unit of energy is named after him.
The exchange between the two is exact only when nothing is lost. A real ball loses some energy to air resistance on the way down, and a bouncing ball loses more to sound and heat at each impact, which is why it never returns to its starting height.
About This Calculator
This calculator solves the kinetic energy equation for energy, speed or mass and the potential energy equation for energy, height or mass, and links the two: every kinetic result shows the drop height that would produce it, and every potential result shows the landing speed. Two more modes give the speed after a fall and the height a throw can reach.
Each value takes its own unit, and every energy is listed in joules, kilojoules, calories, kilocalories, watt-hours, kilowatt-hours, BTU and foot-pounds. Everything runs in your browser; nothing is sent anywhere.
Related tools: Work & Power Calculator, Momentum & Collisions Calculator, and Kinematics (SUVAT) Calculator.
Frequently Asked Questions
What is the difference between kinetic and potential energy?
Kinetic energy is the energy of motion, ½mv². Gravitational potential energy is the energy stored by height, mgh. They trade one for the other: a 1,500 kg car at 100 km/h has 578.7 kJ of kinetic energy, the same as it would gain falling 39.3 m.
Why does doubling the speed quadruple the kinetic energy?
Because speed is squared. The same 1,500 kg car has 144.7 kJ at 50 km/h and 578.7 kJ at 100 km/h, four times as much, which is why stopping distances grow so fast with speed.
Does a heavier object fall faster?
Not without air resistance. In mgh = ½mv² the mass cancels, so v = √(2gh) for any mass: dropped from 20 m, a 0.5 kg ball and a 5 kg ball both land at 19.8 m/s. The heavier one carries ten times the energy, 980.7 J against 98.07 J.
How do I convert joules to kWh or kilocalories?
Divide by 3,600,000 for kilowatt-hours and by 4,184 for kilocalories (food Calories). Raising 1 tonne of water by 100 m stores 980,665 J, which is 0.272 kWh or 234.4 kcal. The calculator shows every unit at once.
Where is zero height for potential energy?
Wherever you choose: only changes in potential energy have a physical meaning. A 2 kg book on a 1.5 m shelf has 29.4 J relative to the floor but 14.7 J relative to a table 0.75 m high. Measure h from the point the object would fall to.
How do I use the Kinetic & Potential Energy Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Road safety
A 1,500 kg car at 100 km/h carries 578.7 kJ, the energy it would have after falling 39.3 m.
Pumped hydro storage
1 tonne of water raised 100 m stores 0.272 kWh, so 1,000 tonnes store 272 kWh before losses.
Sport
A 145 g baseball pitched at 40 m/s carries ½ × 0.145 × 40² = 116 J.
Food energy
A 300 kcal snack is 1,255 kJ: enough, in theory, to lift a 70 kg person 1,828 m if all of it went into climbing.
Physics homework
A 2 kg mass 10 m up has 196.1 J of potential energy and, dropped, lands at 14.0 m/s.
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