What this calculator does
This tool converts between an earthquake's moment magnitude (Mw) and the seismic energy it releases, measured in joules (J), and expresses that energy as an equivalent mass of TNT explosive in metric tons. It is based on the Gutenberg-Richter energy-magnitude relation, a universal physics relationship that applies anywhere on Earth - it is not specific to any country, although it is often illustrated with notable Japanese earthquakes.
How to use it
Pick a conversion direction with the "Convert from" selector. Choose Magnitude to enter a value of M and get the energy in joules plus the TNT equivalent. Choose Energy (J) to enter an energy value with a unit (J through EJ) and get the matching magnitude and TNT mass. The energy unit simply scales your input to SI joules before the formula is applied.
The formula explained
The core relation is $$\log_{10}(J) = 4.8 + 1.5 \times M$$ where J is energy in joules and M is moment magnitude. Solving the other way gives \(M = (\log_{10}(J) - 4.8) / 1.5\). The factor 1.5 means each whole step up in magnitude multiplies the energy by \(10^{1.5} \approx 31.6\) times, and a 2-step jump multiplies it by 1000. For TNT, one metric ton of TNT releases \(4.184 \times 10^9\) J (4.184 GJ), so the equivalent mass is simply J divided by \(4.184\mathrm{e}9\).
Worked example
For a magnitude M = 9.0 earthquake: $$\log_{10}(J) = 4.8 + 1.5 \times 9.0 = 18.3$$ so \(J = 10^{18.3} \approx 1.995 \times 10^{18}\) J (about 2 EJ). The TNT equivalent is $$\frac{1.995\mathrm{e}18}{4.184\mathrm{e}9} \approx 4.77 \times 10^8 \text{ tons}$$ - roughly 477 megatons of TNT.
FAQ
Which magnitude scale is this? It uses moment magnitude (Mw), the modern standard for measuring large earthquakes.
Why does a small magnitude change matter so much? Because energy grows as \(10^{1.5M}\), an increase of just one magnitude unit releases about 31.6 times more energy.
Can I enter negative or very large magnitudes? Yes. The formula is defined for any real M. The energy direction only requires a positive energy value, since the logarithm of zero or a negative number is undefined.
