E = mc² Calculator

How to use this E = mc² calculator

What this calculator does. This calculator evaluates the mass – energy equivalence identity E = mc². It converts a rest mass in kilograms into its equivalent rest energy in joules, and it can invert the same identity to convert an energy value back into an equivalent mass. The speed of light is treated as the exact SI constant 299,792,458 m/s, consistent with the BIPM table of SI defining constants. The result is a physical equivalence, not a claim that an ordinary object can practically release all of its rest energy.

When to use it. Use the calculator to study special relativity, compare the scale of rest energy for different masses, translate a known energy into a mass equivalent, or check textbook and laboratory calculations where mass defects or rest-energy values appear. For particle, nuclear, and fusion contexts, the relevant mass may be a small mass difference rather than the total mass of an object.

How to calculate. The calculator opens with a ready-to-use demonstration: Mass = 1 kg and Energy = 89,875,517,873,681,760 J. The matching XLSX workbook is validated during initialization, so Download Excel is immediately available.

1. To calculate energy from mass, replace the value in Mass. The Energy field and result panel update immediately using E = mc².
2. To calculate mass from energy, edit Energy. The Mass field updates using m = E/c². The field you edit most recently is treated as the source value.
3. Read Rest energy for the energy equivalent, Mass equivalent for the associated mass, and c² conversion factor for the fixed joules-per-kilogram multiplier.
4. Select Download Excel to export the current validated inputs and outputs to a real OOXML workbook. Select Reset to clear the demonstration values and calculated content. After Reset, export is disabled until you enter a complete valid value again.

Input guide. Mass is a non-negative finite decimal number in kilograms. It is required when mass is the source value; examples include 1, 62, 0.001, or scientific notation such as 1e-9. Increasing mass increases rest energy in direct proportion because c² is constant. A common mistake is entering grams as though they were kilograms; convert grams to kilograms first. Empty values, negative values, malformed numbers, ambiguous comma notation, and values that cause a non-finite calculation are rejected. Energy is a non-negative finite decimal number in joules. It is required when energy is the source value; the startup example is 89875517873681760 J. Increasing energy increases the mass equivalent in direct proportion. A common mistake is entering electronvolts or megajoules without first converting them to joules.

Output guide. Rest energy is the equivalent rest energy E in joules, driven by the current mass. A zero mass gives exactly zero rest energy; larger masses produce proportionally larger values. Mass equivalent is m in kilograms, driven by the same canonical model and especially useful when Energy is the field you edit. Zero joules corresponds to zero kilograms. c² conversion factor is the exact constant 89,875,517,873,681,764 J/kg used by the model; it does not change with your inputs. These are identity-based calculations under special relativity, not efficiency estimates or engineering recommendations.

Worked example. With the startup Mass of 1 kg, square the exact speed of light: 299,792,458² = 89,875,517,873,681,764 m²/s². Multiplying by 1 kg gives a Rest energy of 89,875,517,873,681,764 J, displayed compactly as 8.987551787368176 × 10¹⁶ J. Dividing that energy by the same c² value returns a Mass equivalent of exactly 1 kg. This is the same numerical state written into the startup workbook checkpoints.

Learn more. For the underlying physics, the Max Planck Institute's Einstein Online introduction to E = mc² explains why rest mass carries energy. For SI unit definitions, the BIPM overview of the International System of Units describes the defining constants, including the exact value of c.