Earthquake magnitude calculator: energy and size
Compare two earthquake magnitudes. Each whole step on the magnitude scale means waves about 10 times larger on a seismogram and about 32 times more energy released. Uses the formulas the USGS explains, with the working shown below.
Result
31.6 times the energy
A magnitude 7.0 earthquake releases about 31.6 times the energy of a magnitude 6.0, and its waves on a seismogram are 10.0 times larger.
| Magnitude | Energy (joules) | TNT equivalent |
|---|---|---|
| M7.0 | 2.00 × 1015 J | 477 kilotonnes |
| M6.0 | 6.31 × 1013 J | 15.1 kilotonnes |
How it is calculated
The magnitude scale is logarithmic. The USGS explains it like this: one whole unit of magnitude means waves 10 times larger on a seismogram and "approximately 32 times (actually 10**1.5 times) the energy". For two magnitudes M1 and M2:
energy ratio = 10^(1.5 × (M1 − M2)) amplitude ratio = 10^(M1 − M2) energy (joules): log10 E = 1.5 × M + 4.8 TNT (tonnes) = E ÷ 4.184 × 10^9 J
The energy formula is the long-standing Gutenberg-Richter energy-magnitude relation, usually written log E = 1.5M + 11.8 with E in ergs (as in Kanamori, 1977); 4.8 is the same relation in joules. It gives an estimate of the energy radiated as seismic waves, not a measurement. One tonne of TNT is defined as 4.184 × 109 joules.
Worked example: magnitude 7 against magnitude 6
energy ratio = 10^(1.5 × (7 − 6)) = 10^1.5 = 31.6 amplitude ratio = 10^(7 − 6) = 10 energy of M7 = 10^(1.5 × 7 + 4.8) = 10^15.3 = 2.00 × 10^15 J TNT equivalent = 2.00 × 10^15 ÷ 4.184 × 10^9 = 477 kilotonnes
So an M7 earthquake releases about 32 times the energy of an M6. Two whole steps, such as M8 against M6, is 103 = 1,000 times the energy.
Reference table
| Magnitude | Energy (joules) | TNT equivalent | Energy compared with one magnitude less |
|---|---|---|---|
| M3 | 2.00 × 109 | 0.477 tonnes | × 31.6 |
| M4 | 6.31 × 1010 | 15.1 tonnes | × 31.6 |
| M5 | 2.00 × 1012 | 477 tonnes | × 31.6 |
| M6 | 6.31 × 1013 | 15.1 kilotonnes | × 31.6 |
| M7 | 2.00 × 1015 | 477 kilotonnes | × 31.6 |
| M8 | 6.31 × 1016 | 15.1 megatonnes | × 31.6 |
| M9 | 2.00 × 1018 | 477 megatonnes | × 31.6 |
Magnitude is the size of the earthquake at its source. How strongly the ground shakes where you are also depends on distance, depth and the ground itself, which is why two earthquakes of the same magnitude can do very different harm.
This calculator gives an estimate for learning and planning. It is not a forecast or a warning, and it cannot say whether conditions are safe. For decisions, follow your national weather service and local authorities.
Sources
- USGS: How much bigger is a magnitude 8.7 earthquake than a magnitude 5.8?: amplitude 10^ΔM, energy 10^(1.5ΔM), "approximately 32 times" per unit
- USGS: The Severity of an Earthquake: tenfold amplitude and about 31 times the energy per whole number
- Kanamori, H. (1977), The energy release in great earthquakes, Journal of Geophysical Research 82(20), 2981-2987: the standard energy-magnitude relation log E = 1.5M + 11.8 (ergs)
- NIST Guide to the SI (SP 811), Appendix B.8: ton of TNT (energy equivalent) = 4.184 × 10^9 J
Questions
How much stronger is a magnitude 7 than a magnitude 6 earthquake?
A magnitude 7 releases about 32 times the energy of a magnitude 6 (10 to the power 1.5, which is 31.6), and its waves on a seismogram are 10 times larger. Two whole magnitudes is about 1,000 times the energy.
Is magnitude the same as how strong the shaking is?
No. Magnitude is the size of the earthquake at its source. The shaking you feel also depends on how far away and how deep it was and on the ground under you; that is measured on intensity scales, not magnitude.
What does the TNT figure mean?
It turns the estimated energy into tonnes of TNT so very large and very small numbers can be compared. It is an estimate from a long-used formula, not a measurement of the earthquake, and it says nothing about damage.