Energy Calculator — KE, PE, Thermal & Electrical

Calculate kinetic energy (½mv²), gravitational PE (mgh), elastic PE (½kx²), thermal energy (mcΔT), and electrical energy (Pt). Convert between energy forms and units.

Energy Type

Solve for

Mass (kg)

Velocity (m/s)

Output Energy Unit

Enter calculate · Esc reset

What Is the Energy Calculator — KE, PE, Thermal & Electrical?

The Energy Calculator covers six fundamental energy formulae — kinetic, gravitational potential, elastic potential, thermal, electrical, and mechanical work — in one unified tool. Select the energy type, choose which variable to solve for, enter the remaining values, and get the result in any of nine energy units instantly.

›Six energy types — kinetic (½mv²), gravitational PE (mgh), elastic PE (½kx²), thermal (mcΔT), electrical (Pt), and work (Fd cos θ), each with its own input layout.
›Solve for any variable — for kinetic energy you can solve for KE, mass, or velocity; for gravitational PE you can solve for PE, mass, height, or g. Every energy type supports full bidirectional solving.
›Nine output energy units — results are shown in J, kJ, MJ, Wh, kWh, kcal, BTU, eV, and ft·lb simultaneously in a responsive conversion grid.
›Material presets for thermal energy — a built-in specific-heat table covers water, aluminium, iron, copper, and air so you don't need to look up c values.
›Gravity selector for PE — choose from Earth, Moon, Mars, or Jupiter surface gravity, or enter a custom value for any other body.
›Step-by-step working — a collapsible panel shows the formula, substitution, and result with full unit labelling at every step.

Formula

This calculator covers six fundamental energy forms. Each has its own formula, variable set, and solve-for options. All results are expressed in joules and converted to your chosen output unit.

Kinetic Energy

KE = ½mv²

m = mass (kg), v = velocity (m/s)

Gravitational PE

PE = mgh

g = gravity (m/s²), h = height (m)

Elastic PE

PE = ½kx²

k = spring constant (N/m), x = extension (m)

Thermal Energy

Q = mcΔT

c = specific heat J/(kg·°C), ΔT = temperature change

Electrical Energy

E = Pt = VIt

P = power (W), t = time (s), V = voltage, I = current

Work Done

W = Fd cos(θ)

F = force (N), d = displacement (m), θ = angle

Symbol	Name	Description
m	Mass	Object mass in kilograms
v	Velocity	Speed in metres per second for KE
g	Gravitational acceleration	Earth: 9.81 m/s², Moon: 1.62 m/s², Mars: 3.72 m/s²
h	Height	Vertical displacement above reference level (metres)
k	Spring constant	Stiffness of spring or elastic material in N/m
x	Extension / compression	Deformation from natural length in metres
c	Specific heat capacity	Energy per unit mass per degree: J/(kg·°C)
ΔT	Temperature change	Final minus initial temperature in °C (or K — same difference)
P	Power	Rate of energy transfer in watts (W = J/s)
t	Time	Duration of energy transfer in seconds
V	Voltage	Electric potential difference in volts
I	Current	Electric current in amperes
F	Force	Applied force magnitude in newtons
d	Displacement	Distance over which force acts, in metres
θ	Angle	Angle between force direction and displacement vector (degrees)

How to Use

1
Select the energy type: Click one of the six orange pill tabs: Kinetic, Gravitational PE, Elastic PE, Thermal, Electrical, or Work.
2
Choose what to solve for: Use the "Solve for" dropdown to select the unknown variable. The input fields update automatically to show only the required inputs.
3
Enter the known values: Type your values into the labeled fields. For thermal energy, pick a material preset to auto-fill the specific heat. For gravitational PE, select a planetary body or enter a custom g.
4
Select the output energy unit: Use the output unit dropdown to choose J, kJ, kWh, kcal, BTU, or another unit. The result and all unit conversions update instantly.
5
Calculate and review: Click Calculate or press Enter. The primary result appears in large orange text, followed by a full unit-conversion grid and a step-by-step breakdown.

Example Calculation

Example 1 — Kinetic energy of a car at motorway speed

A 1,500 kg car travels at 100 km/h (27.78 m/s). Calculate its kinetic energy and express it in kJ and kWh.

Given: m = 1500 kg, v = 100 km/h = 27.78 m/s

KE = ½ × m × v²

= 0.5 × 1500 × (27.78)²

= 0.5 × 1500 × 771.73

KE = 578,798 J ≈ 578.8 kJ ≈ 0.1608 kWh

This is roughly equivalent to the energy in 138 kcal — about one chocolate bar — which must be dissipated entirely as heat in the brakes when the car stops.

Example 2 — Gravitational PE of a ball on a shelf

A 0.5 kg ball sits on a shelf 10 m above the floor. What is its gravitational potential energy?

Given: m = 0.5 kg, g = 9.81 m/s², h = 10 m

PE = m × g × h

= 0.5 × 9.81 × 10

PE = 49.05 J ≈ 49.05 J ≈ 11.72 cal

Conservation of energy

If the ball is dropped, its 49.05 J of PE converts entirely to KE just before impact (ignoring air resistance): ½mv² = 49.05 J → v = √(2 × 49.05 / 0.5) = √196.2 ≈ 14.0 m/s. This is the same result you get from SUVAT (v² = 2gh = 2×9.81×10 = 196.2).

Understanding Energy — KE, PE, Thermal & Electrical

The Law of Conservation of Energy

The most fundamental principle in all of physics is that energy can neither be created nor destroyed — it can only be converted from one form to another or transferred between objects. This is the First Law of Thermodynamics applied broadly: the total energy of an isolated system is constant.

›A falling ball converts gravitational PE → KE → sound and heat on impact.
›An electric motor converts electrical energy → mechanical (kinetic) energy → work done.
›A compressed spring converts elastic PE → KE when released.
›A braking car converts KE → thermal energy in the brake pads and tyres.

Practical implication

Conservation of energy allows you to skip the mechanics entirely in some problems. For a ball dropped from height h, you don't need SUVAT — just set PE = KE: mgh = ½mv², giving v = √(2gh). The mass cancels, showing all objects fall at the same speed (in a vacuum) — precisely what Galileo demonstrated at the Leaning Tower of Pisa.

Comparing Energy Types

Type	Formula	Stored in…	Converts to…
Kinetic	KE = ½mv²	Moving mass	PE (rising), heat (friction)
Gravitational PE	PE = mgh	Height above reference	KE (falling), work
Elastic PE	PE = ½kx²	Stretched/compressed spring	KE, acoustic energy
Thermal	Q = mcΔT	Molecular motion	Work (engine), radiation
Electrical	E = Pt	Charge flow	Thermal (resistance), KE (motor), light
Work	W = Fd cos θ	Agent doing the pushing	KE, PE, heat (depends on system)

Kinetic vs Potential Energy

Kinetic and potential energy are complementary. Kinetic energy is energy of motion; potential energy is stored energy due to position or configuration. In a closed mechanical system the total mechanical energy E = KE + PE is constant:

At any point during a frictionless swing:

½mv² + mgh = constant

At the bottom: all KE, no PE → v is maximum

At the top: all PE, no KE → v = 0 momentarily

In real systems, friction converts some mechanical energy into heat, gradually reducing the total mechanical energy available but not violating conservation — the heat is simply a harder-to-recover form of energy.

Energy Efficiency and Real Systems

Efficiency (η) is the ratio of useful energy output to total energy input, expressed as a percentage: η = (E_useful / E_input) × 100%. No real device achieves 100% efficiency because every energy conversion produces some waste heat.

›Electric motors: 85–97% efficient — best of all common machines. Most losses are resistive heat (I²R) in windings.
›Internal combustion engines: 25–40% — most fuel energy becomes exhaust heat, not mechanical work.
›LED lights: 40–60% — convert electrical energy to light; incandescent bulbs were only ~5% efficient.
›Solar panels: 15–23% (silicon photovoltaic) — remaining solar energy reflects or becomes heat in the panel.
›Heat pumps: 250–400% COP (coefficient of performance) — they move heat rather than generate it, so they can deliver more energy than they consume electrically.

Energy Units Explained

The SI unit of energy is the joule (J) — defined as the work done by a force of one newton acting through one metre. All other common energy units are fixed multiples of joules:

›1 kJ = 1,000 J — used for everyday engineering and food energy contexts.
›1 kWh = 3,600,000 J = 3.6 MJ — the unit on your electricity bill (power × time).
›1 kcal = 4,184 J — the "Calorie" on food labels (note: 1 food Calorie = 1 kcal, not 1 cal).
›1 BTU ≈ 1,055.06 J — British Thermal Unit, still used in HVAC in the United States.
›1 eV = 1.602×10⁻¹⁹ J — the natural unit in atomic and particle physics.
›1 ft·lb ≈ 1.3558 J — used for torque and impact energy in US engineering.

Frequently Asked Questions

What is the difference between kinetic and potential energy?

›KE = ½mv² — increases with the square of velocity. Doubling speed quadruples KE.
›Gravitational PE = mgh — proportional to both mass and height above a reference level.
›Elastic PE = ½kx² — proportional to the square of deformation; a stiffer spring (larger k) stores more energy for the same stretch.

In a pendulum or roller coaster (no friction), energy oscillates between PE and KE. At the lowest point, all energy is kinetic. At the highest point, all is potential. Real systems lose some energy to heat via friction and air resistance.

Which value of g should I use for gravitational PE?

Standard values of gravitational acceleration at the surface:

›Earth: 9.81 m/s² (engineering standard) or 9.80665 m/s² (ISO exact standard gravity)
›Moon: 1.62 m/s² — 16.5% of Earth gravity
›Mars: 3.72 m/s² — 38% of Earth gravity
›Jupiter: 24.79 m/s² — 2.53× Earth gravity

For satellite or high-altitude problems, use g = GM/r² where r is the distance from Earth's centre (6,371 km + altitude). This calculator offers a custom g input for exactly this case.

What is the difference between thermal energy and heat?

›Thermal energy (U) — internal energy of a system; proportional to temperature.
›Heat (Q) — energy crossing a system boundary due to a temperature difference.
›Q = mcΔT — the sensible heat equation: c is specific heat capacity (J/kg·°C), ΔT is the temperature change.
›Latent heat (not in this calculator) — energy for phase changes (melting, boiling) at constant temperature.

Specific heat values: water = 4186, aluminium = 897, iron = 449, copper = 386, air ≈ 1005 J/(kg·°C). Water has the highest specific heat of common substances, making it an excellent coolant.

Does the law of conservation of energy always hold?

Energy conservation holds universally:

›Mechanical systems: KE + PE = constant in frictionless systems; friction converts some to heat.
›Chemical reactions: bond energy converts to kinetic energy of products and radiated heat.
›Nuclear reactions: E = mc² — mass defect releases energy, extending the conservation law.
›Quantum mechanics: conservation holds exactly even at the subatomic level (Noether's theorem).

The only apparent exception is quantum uncertainty (ΔEΔt ≥ ℏ/2), which allows brief energy fluctuations but these average out — energy is conserved on measurable timescales.

Can an object's kinetic energy equal its gravitational PE?

Setting KE = PE gives a very useful result for free fall and projectile problems:

½mv² = mgh

v² = 2gh

Mass cancels — all objects fall the same speed from height h (vacuum)

›From h = 10 m: v = √(2 × 9.81 × 10) ≈ 14.0 m/s at impact.
›From h = 100 m: v = √(2 × 9.81 × 100) ≈ 44.3 m/s (a significant impact speed).
›This equality forms the basis of the work–energy theorem: W_net = ΔKE.

What is the difference between electrical energy and power?

›Power (P, watts) — rate of energy use: how fast energy flows. P = VI = I²R = V²/R.
›Energy (E, joules) — total amount transferred: E = Pt = VIt.
›1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 MJ.
›A smartphone charger at 18 W for 2 hours uses 18 × 7200 = 129,600 J ≈ 0.036 kWh.

The distinction matters for billing: the electricity meter measures kWh (energy), not watts (instantaneous power). Two devices with the same wattage use the same energy only if run for the same time.