Formula of Energy: KE, PE and Other Energy Formulas in Physics

The formula of energy you will use most often is the mechanical energy of a moving, raised object, $E = \frac{1}{2}mv^2 + mgh$ : kinetic energy from its speed plus potential energy from its height. Energy measures how much work something can do, it is a scalar, and its SI unit is the joule (J).

There is no single energy formula in physics, because energy comes in many forms and each has its own expression. Class 10 students mainly need $KE = \frac{1}{2}mv^2$ and $PE = mgh$ . Later chapters add electrical energy $E = Pt$ , heat $Q = mc\Delta T$ , photon energy $E = hf$ and mass energy $E = mc^2$ . This page gathers them in one table, works one example per form and explains why every one of them ends up in joules.

Quick facts

Mechanical energy
$E = \frac{1}{2}mv^2 + mgh$
Kinetic energy
$K = \frac{1}{2}mv^2$
Gravitational potential energy
$U = mgh$ near Earth's surface
SI unit
joule (J) = kg m²/s²
Dimensional formula
[M¹ L² T⁻²]
Type
Scalar
Other units
1 kWh = 3.6 × 10⁶ J, 1 eV = 1.602 × 10⁻¹⁹ J, 1 cal = 4.186 J

Energy formulas physics students need, in one table

Forms of energy and their formulas
Form	Formula	Symbols
Kinetic	$K = \frac{1}{2}mv^2$	m mass (kg), v speed (m/s)
Gravitational potential	$U = mgh$	g = 9.8 m/s², h height (m)
Elastic (spring)	$U = \frac{1}{2}kx^2$	k spring constant (N/m), x stretch (m)
Electrical	$E = Pt = VIt$	P power (W), t time (s), V voltage, I current
Heat	$Q = mc\Delta T$	c specific heat (J/(kg K)), ΔT temperature change
Photon	$E = hf$	h = 6.626 × 10⁻³⁴ J s, f frequency (Hz)
Mass energy	$E = mc^2$	c = 3.00 × 10⁸ m/s

Each row has its own page where you need more detail: kinetic energy, potential energy, spring potential energy, heat and the mass energy relation.

Formula of energy class 10: kinetic and potential

Kinetic energy is the energy of motion. A body of mass m moving at speed v has $K = \frac{1}{2}mv^2$ . Because the speed term is squared, a body going twice as fast carries four times the kinetic energy. That is why a car at 80 km/h needs about four times the braking distance it needs at 40 km/h, for the same braking force.

Potential energy is stored energy due to position. Lifting a mass m through a height h against gravity stores $U = mgh$ . The height is measured from whatever level you choose as zero, so only changes in potential energy have a fixed meaning.

Their sum is the mechanical energy, $E = K + U$ . When only gravity does work, E stays constant, which is the principle on the conservation of energy formula page.

Worked examples using the formula of energy

Example 1: a bird in flight

A 0.50 kg bird flies at 10 m/s at a height of 20 m. Find its kinetic, potential and total mechanical energy.

$K = \frac{1}{2}(0.50)(10)^2 = 25\ \text{J}$

$U = (0.50)(9.8)(20) = 98\ \text{J}$

$E = 25 + 98 = 123\ \text{J}$

The calculator on this page gives the same 123 J if you enter m = 0.50, v = 10 and h = 20.

Example 2: an electric heater, with a unit change

A 1.5 kW heater runs for 2.0 hours. How much electrical energy does it use, in kWh and in joules?

$E = Pt = 1.5\ \text{kW} \times 2.0\ \text{h} = 3.0\ \text{kWh}$

$3.0 \times 3.6 \times 10^{6} = 1.08 \times 10^{7}\ \text{J}$

Example 3: energy of one photon

Find the energy of a photon of light with frequency 5.0 × 10¹⁴ Hz.

$E = hf = (6.626 \times 10^{-34})(5.0 \times 10^{14}) = 3.3 \times 10^{-19}\ \text{J}$

Divide by 1.602 × 10⁻¹⁹ to get about 2.1 eV.

Example 4: mass turned into energy

How much energy is released if 2.0 g of mass is completely converted?

$E = (2.0 \times 10^{-3}\ \text{kg})(9.00 \times 10^{16}\ \text{m}^2/\text{s}^2) = 1.8 \times 10^{14}\ \text{J}$

Convert grams to kilograms first, or the answer is a thousand times too big.

Why every energy has the same unit

Take kinetic energy: kg × (m/s)² = kg m²/s². Potential energy mgh gives kg × m/s² × m, the same thing. This unit is the joule, and its dimensional formula [M¹ L² T⁻²] is shared by work, heat and every other form. The dimensional formula of energy page shows the derivation in full.

This shared unit is what makes energy so useful. Energy can change from one form to another, from chemical to electrical in a cell or from potential to kinetic in a falling ball, and the total can be tracked in joules throughout. Energy is transferred by doing work, which is why the work formula gives an answer in joules too.

Mistakes with energy questions

Squaring the mass instead of the speed in ½mv².
Forgetting the ½ in kinetic or spring energy.
Using grams or km/h. Convert to kg and m/s before substituting.
Treating energy as a vector. It has no direction, so energies just add as numbers.
Mixing up power and energy. Power is energy per second, in watts; energy is in joules or kWh.

The whole chapter, from work to collisions, is laid out page by page on the work and energy hub.

Frequently asked questions

Which energy formulas do physics problems use most?

It depends on the form. Kinetic energy is ½mv², gravitational potential energy is mgh, and mechanical energy is their sum, E = ½mv² + mgh. Other forms include E = Pt, E = hf and E = mc².

What is the SI unit of energy?

The joule (J), equal to one kilogram metre squared per second squared. Larger amounts are often given in kilowatt hours, where 1 kWh = 3.6 × 10⁶ J.

Is energy a scalar or a vector?

Energy is a scalar. It has size but no direction, so energies of different parts of a system can be added directly.

What is the formula of energy for Class 10?

The two main ones are kinetic energy KE = ½mv² and potential energy PE = mgh. Class 10 electricity also uses electrical energy E = Pt = VIt.

What is the difference between energy and power?

Energy is how much work can be done, in joules. Power is how quickly energy is transferred, in watts, with P = E / t.