Decay Energy Calculator - Calculator Academy

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

Decay Energy Formula

The decay energy calculator uses Einstein’s mass-energy relationship. The energy released in a decay is based on the loss of mass during the decay process.

E = (m_b - mₐ)c²

Rearranged formulas used by the calculator:

m_b = E / c² + mₐ

mₐ = m_b - 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, taken as 3 × 10⁸ m/s

The calculator lets you enter any two values and solves for the missing one. If you enter mass before decay and mass after decay, it calculates decay energy. If you enter decay energy and one mass value, it rearranges the same formula to find the missing mass.

Mass values are converted to kilograms before calculation. Energy values are converted to joules before calculation. The result is then converted back to the unit selected for the missing field.

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	0.453592 kg
Energy	1 J	1 J
Energy	1 kJ	1,000 J
Energy	1 MJ	1,000,000 J

Mass Defect and Energy Relationship

Mass lost	Energy released	Meaning
1 kg	9 × 10¹⁶ J	Very large energy release
1 g	9 × 10¹³ J	Energy from 0.001 kg of mass loss
1 mg	9 × 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)(3*10⁸)²

E = 0.001 * 9*10¹6 = 9*10¹3 J

The decay energy is 9 × 10¹³ J.

Example 2: Calculate mass after decay

You have a mass before decay of 5 kg and a decay energy of 9 × 10¹⁶ J.

mₐ = 5 - (9*10¹6) / (3*10⁸)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 decay energy means the mass after decay is greater than the mass before decay in the entered values. For a normal energy-releasing decay calculation, mass before decay should be greater than mass after decay. Check your values and units if you get a negative result.

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.