Calculate decay energy, mass before decay, or mass after decay from any two values using mass-energy equivalence and unit conversions.

Find energy released from a nonnegative mass difference.

Use rest masses of all initial and final particles on a consistent atomic or nuclear basis. Final mass includes every decay product; this does not predict a decay pathway.

Decay Energy Formula

The decay energy calculator uses Einstein’s mass-energy relationship. The released energy is the difference between the initial rest mass and the sum of all final product rest masses, multiplied by c². Include every emitted particle and use consistent nuclear or atomic masses with the same electron accounting. This arithmetic does not identify which decay pathways are possible.

E = (mb - mₐ)c²

Rearranged formulas used by the calculator:

mb = E / c² + mₐ
mₐ = mb - E / c²
  • E = decay energy, in joules J
  • m_b = mass before decay, in kilograms kg
  • m_a = mass after decay, in kilograms kg
  • c = speed of light in vacuum, exactly 299,792,458 m/s

Select decay energy, mass before decay, or mass after decay and enter the other two values. Choose the result unit separately. Zero energy and zero mass limits are allowed; negative released energy or an implied negative product mass is rejected.

Mass values are converted to kilograms before calculation. Energy values are converted to joules before calculation. The result is converted to the selected result unit. Very small values use scientific notation; the precision of small differences between large masses is limited by the inputs and floating-point arithmetic.

Common Unit Conversions for Decay Energy Calculations

Quantity Unit Conversion to base unit
Mass 1 kg 1 kg
Mass 1 g 0.001 kg
Mass 1 lb 0.45359237 kg
Energy 1 J 1 J
Energy 1 kJ 1,000 J
Energy 1 MJ 1,000,000 J

Mass Defect and Energy Relationship (rounded energies)

Mass lost Energy released Meaning
1 kg 8.98755 × 1016 J Very large energy release
1 g 8.98755 × 1013 J Energy from 0.001 kg of mass loss
1 mg 8.98755 × 1010 J Energy from 0.000001 kg of mass loss

Example Decay Energy Calculations

Example 1: Calculate decay energy

You have a mass before decay of 2.000 kg and a mass after decay of 1.999 kg.

E = (2.000 - 1.999)(299792458)²
E = 0.001 × 89875517873681764 ≈ 8.98755 × 10¹3 J

The decay energy is 8.98755 × 1013 J.

Example 2: Calculate mass after decay

You have a mass before decay of 5 kg and a decay energy of exactly 89,875,517,873,681,764 J (about 8.98755 × 1016 J).

mₐ = 5 - (89875517873681764) / (299792458)²
mₐ = 5 - 1 = 4 kg

The mass after decay is 4 kg.

FAQ

Why does a small mass difference produce a large amount of energy?

The formula multiplies the mass difference by the speed of light squared. Since the speed of light is very large, c2 is about 9 × 1016. That makes even a small mass defect correspond to a large energy value.

What does it mean if the calculated decay energy is negative?

A negative mass difference means the total product rest mass exceeds the initial rest mass, corresponding to required rather than released energy. This released-energy model rejects that case. Check your mass sums and units; a zero difference gives zero released energy.

Which units should you use?

You can enter mass in kg, g, or lb and energy in J, kJ, or MJ. The calculation itself is based on kilograms and joules, so using kg and J makes the formula easiest to check by hand.