Why use this calculator
Energy is the quantity that links problems which look unrelated: a braking car, a raised load, a heated room and an electricity bill are all measured in the same unit once you convert properly. The trouble is that every field uses its own unit and several of them are named confusingly, with the dietary calorie actually being a kilocalorie and the kilowatt-hour being an energy while the kilowatt is a rate.
This calculator does the physics and the conversions in one step, so a result can be quoted in joules for a report, kilowatt-hours for a utility comparison or BTU for a heating specification without a second round of arithmetic. It also uses standard gravity of 9.80665 m/s² exactly rather than the rounded 9.81, which keeps results consistent with published tables.
How to use it
- Choose the energy type first, because that decides which inputs appear and which formula is applied.
- For kinetic energy, enter the mass in kilograms and the velocity in metres per second, converting from km/h by dividing by 3.6 before you type it.
- For potential energy, enter the mass and the vertical height above whatever reference level you have chosen, then pick the gravitational field if you are not on Earth.
- For work done, enter the force in newtons, the distance the object actually moved, and the angle between the force and that movement, which is zero when you push straight along the direction of travel.
- Read the joule figure first, then take whichever converted unit your report needs.
What each result means
- Energy
- The result in joules, the SI unit of energy and of work, equal to one newton-metre.
- In kilojoules
- The same figure in thousands of joules, the usual unit for food labels and process heat.
- In kilowatt-hours
- The energy as an electricity meter would record it, useful for costing anything that runs on power.
- In kilocalories
- The same energy in dietary calories, where one food calorie is one thousand small calories.
- In BTU
- British thermal units, still the standard unit for heating and air conditioning equipment ratings.
- In foot-pounds
- The imperial energy unit used in ballistics and older mechanical engineering literature.
- Lifting equivalent
- How high one kilogram could be raised with this energy, giving a physical sense of scale.
The formula
Kinetic energy
KE = ½ m v²
Gravitational potential energy
PE = m g h
Work
W = F d cos θ
One joule is one newton-metre.
Conversions used:
- 1 kWh = 3,600,000 J
- 1 kcal = 4,184 J
- 1 BTU = 1,055.05585262 J
- 1 foot-pound = 1.3558179483314004 J
How this number is used in practice
Crash safety is the clearest demonstration of the square law in the kinetic energy formula. A 1,500 kg car at 50 km/h carries about 145 kJ; at 100 km/h it carries roughly 579 kJ, four times as much, and every joule of it has to be absorbed by crumple zones, barriers and occupants.
That is why impact severity rises far faster than speed, and why speed limits do so much work in injury statistics. Engineers designing lifts, cranes and fall-arrest systems run the potential energy version of the same sum: a 100 kg worker falling two metres arrives with about 1,961 J, and the harness and lanyard have to dissipate it over a distance long enough to keep the arresting force survivable.
In building services and energy analysis the conversions matter as much as the physics. Heating equipment is still specified in BTU across much of the world while electricity is billed in kilowatt-hours, so comparing a gas heater with a heat pump means moving between the two.
A facilities manager who knows a process needs 50 MJ a day can convert that to 13.9 kWh and price it directly from the tariff. The unit trap to watch is power against energy: a kilowatt is a rate and a kilowatt-hour is a quantity, so a 2 kW heater running for three hours uses 6 kWh, and confusing the two is the most common error in energy reporting.
Worked examples
A 10 kg mass moving at 5 m/s
125.000 J of kinetic energy, which is 0.02988 kilocalories.
A 2 kg book lifted 10 m onto a shelf on Earth
196.133 J of gravitational potential energy.
Pulling a sled with 500 N along a rope at 30° over 10 m
4,330.13 J of work, since only the component along the motion counts.
When people use it
- Comparing impact energy at different speeds for vehicle or machine guarding assessments
- Sizing fall-arrest equipment from the potential energy a fall would release
- Converting a process energy requirement from joules into kilowatt-hours for costing
- Checking physics homework on kinetic energy, potential energy and work
- Translating a heating requirement between BTU, kilojoules and kilowatt-hours
Tips
- Kinetic energy depends on the square of the speed, so doubling speed quadruples the energy that must be absorbed in a stop.
- Enter velocity in metres per second. Divide a km/h figure by 3.6 and a mph figure by 2.237 before you type it.
- A kilowatt is a rate of energy use and a kilowatt-hour is a quantity of energy. A 2 kW heater for 3 hours uses 6 kWh.
- The dietary calorie on a food label is really a kilocalorie, which is 4,184 joules, not 4.184.
- A force at right angles to the motion does no work, which is why carrying a box across a level floor costs no work in the physics sense.
- Only the change in height matters for potential energy, so pick a reference level and stay consistent with it.
What it assumes, and where it stops being accurate
- Classical mechanics is assumed, so results are wrong for speeds approaching the speed of light.
- The gravitational field is treated as uniform, which is fine near the surface but not for orbital or deep-space heights.
- Friction, air resistance and drivetrain losses are ignored, so real systems need more energy than the ideal figure.
- Mass is constant during the motion; rockets and anything else that sheds mass need a different treatment.
- Work is calculated for a constant force along a straight path. A varying force requires integration rather than a single multiplication.
Terms used on this page
- Joule (J)
- The SI unit of energy: the work done by one newton acting through one metre.
- Kinetic energy
- Energy an object has because it is moving, equal to half the mass times velocity squared.
- Conservative force
- A force, such as gravity, where the work done depends only on start and end points.
- Kilowatt-hour
- The energy of one kilowatt sustained for one hour, equal to 3.6 megajoules.
Questions people ask
- What is the relationship between work and energy?
- Work is energy transferred by a force acting through a distance, and the two share the same unit, the joule. The work-energy theorem says the net work done on an object equals its change in kinetic energy, so pushing a trolley harder over the same distance leaves it moving faster because the extra work became extra kinetic energy.
- Why does doubling speed quadruple the energy?
- Because velocity is squared in the kinetic energy formula. Energy is proportional to v², so twice the speed gives four times the energy and three times the speed gives nine times. This is why stopping distances grow so quickly with speed and why high-speed impacts are so much more severe than the speed difference suggests.
- What is the difference between a calorie and a kilocalorie?
- A small calorie is 4.184 joules and raises one gram of water by one degree Celsius. A kilocalorie is a thousand of those, or 4,184 joules. Food labelling uses kilocalories but usually writes them as Calories with a capital C, which is why a 2,000 Calorie diet is really 2,000 kilocalories or about 8.4 megajoules.
- How do I convert joules to kilowatt-hours?
- Divide by 3,600,000, because one watt-hour is one joule per second sustained for 3,600 seconds and a kilowatt-hour is a thousand of those. So one megajoule is about 0.278 kWh. The calculator does this conversion automatically, which makes costing an energy requirement against a tariff straightforward.
- Does potential energy depend on the path taken?
- No. Gravity is a conservative force, so only the vertical change in height matters. Carrying a load up a long ramp and lifting it straight up the same height need identical work against gravity, although the ramp adds friction losses that the ideal formula does not include.
- Why is standard gravity 9.80665 rather than 9.81?
- Because 9.80665 m/s² is the conventional standard value adopted internationally for calibration and definitions, while local gravity actually varies from about 9.78 at the equator to 9.83 at the poles. Using the defined constant keeps results consistent with published tables; for precision work, use your locally measured value instead.
Use this with
Energy Calculator answers one part of the question. These pick up where it stops: Ohm's Law Calculator, Power Bill Calculator, Speed Distance Time Calculator and HVAC BTU Calculator.
Where these figures come from
This calculation is jurisdiction-neutral arithmetic. No country-specific rules are applied.
- NIST: CODATA fundamental physical constants. Recommended values of the physical constants
- NIST Special Publication 811: Guide for the Use of the SI. Exact conversion factors and correct unit style
- US Energy Information Administration. Energy unit conventions and consumption data
Energy Calculator produces an estimate for general information. It is not financial, tax, medical, legal or engineering advice. read the full disclaimer. Spotted a wrong number? Report it and it gets fixed. The form picks up this calculator and the inputs you used.