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Mass–energy equivalence calculator

A-level Nuclear and particles

The energy equivalent of a mass, used in nuclear reactions to find the energy released from a mass difference.

E = m c²

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

EEnergy released to find 2.70 × 10⁻¹² J

mMass converted to energy

cSpeed of light constant m/s

Significant figures

Working

Write the equation
E = m c²
Constants used
c = 3 × 10⁸ m/s
Substitute the values
E = (3 × 10⁻²⁹) × (3 × 10⁸)²
Calculate
E = 2.7 × 10⁻¹² J
Give the answer to 3 significant figures
E = 2.70 × 10⁻¹² J

Worked example

Find E, the energy released. Given: mass converted to energy m = 3.00 × 10⁻²⁹ kg; speed of light c = 3 × 10⁸ m/s.

Write the equation
E = m c²
Constants used
c = 3 × 10⁸ m/s
Substitute the values
E = (3 × 10⁻²⁹) × (3 × 10⁸)²
Calculate
E = 2.7 × 10⁻¹² J
Give the answer to 3 significant figures
E = 2.70 × 10⁻¹² J

Symbols and units

Symbol	Quantity	SI unit
E	Energy released	J
m	Mass converted to energy	kg
c	Speed of light (constant)	m/s

Mass–energy equivalence: rearranged

To find energy released: E = m c²
To find mass converted to energy: m = E / c²

Exam tip

In nuclear equations, use the mass defect in kg. 1 u is 1.66 × 10⁻²⁷ kg.

Common questions

What is the formula for mass–energy equivalence?

The equation is E = m c², where E is the energy released (J); m is the mass converted to energy (kg); c is the speed of light (m/s).

What units should I use for mass–energy equivalence?

In SI units: energy released in J, mass converted to energy in kg, speed of light in m/s. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange E = m c²?

Rearranging gives these forms: to find energy released: E = m c². to find mass converted to energy: m = E / c².

Practise mass–energy equivalence questions

Include unit conversions (km, g, minutes…)

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Read the full explanation on the Mass–energy equivalence formula page. More nuclear and particles equations: Photon energy, Photon energy from wavelength, Photoelectric equation, de Broglie wavelength, Radioactive decay and half-life, Activity and decay constant, Half-life and decay constant. See the full list on the a-level physics equation calculator page.