Earthquake Magnitude & Energy Calculator

Understanding the earthquake magnitude and energy calculator — concept and principle

Earthquake magnitude is a logarithmic number, so a difference of one or two units hides a huge difference in size. This calculator compares two magnitudes, showing how much more ground-motion amplitude and radiated seismic energy the larger one has, and converts the energy of the first quake into joules and kilotons of TNT. It helps put news reports and historical earthquakes in perspective.

One step of magnitude means 10× the shaking but 31.6× the energy.

How it is calculated

Amplitude ratio = 10^(M1 − M2)
Energy ratio = 10^(1.5 × (M1 − M2))
Energy of M1: log₁₀E = 1.5 × M1 + 4.8, with E in joules
TNT equivalent = E ÷ 4.184 × 10¹² J per kiloton

M1 and M2 are magnitudes on the same scale; the inputs have no units.

The principle

Charles Richter defined magnitude as the base-10 logarithm of the amplitude recorded on a standard seismograph, so one unit always means ten times the amplitude. Energy, however, grows faster than amplitude. Beno Gutenberg and Richter fitted the relation log₁₀E = 1.5M + 4.8 to observed earthquakes, which means each magnitude unit carries 10^1.5 ≈ 31.6 times more energy, and two units 1,000 times more. The constant 4.8 sets the absolute scale in joules. A kiloton of TNT is defined as 4.184 × 10¹² J.

Worked example

Inputs: M1 = 7, M2 = 6, difference 1.
Amplitude ratio: 10¹ = 10.
Energy ratio: 10^1.5 = 31.6227766.
Energy of M1: 1.5 × 7 + 4.8 = 15.3, so E = 10^15.3 ≈ 1.995262 × 10¹⁵ J.
TNT: 1.995262 × 10¹⁵ ÷ 4.184 × 10¹² ≈ 476.88 kt (476.8791384).

Each point is the calculator re-run with only “Magnitude 1” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Magnitude 1	Energy ratio
1.75	4.216965e-7
3.5	0.0001778279
5.25	0.0749894209
7	31.6227766
8.75	13,335.21432
10.5	5,623,413.252
14	1,000,000,000,000

How to read the result

A magnitude 7 releases roughly the energy of half a megaton of TNT, which is why such earthquakes can damage entire regions. Going from 6 to 8 multiplies the energy by 1,000. Remember that the energy figure is the radiated seismic wave energy; the total energy spent on breaking rock and producing heat is larger and not estimated here.

Common mistakes

Assuming magnitude 8 is "twice as strong" as magnitude 4; it is 10,000 times the amplitude and a million times the energy.
Confusing magnitude with intensity scales such as the Modified Mercalli or JMA seismic intensity, which describe local shaking.
Comparing magnitudes from different scales (local ML, surface-wave Ms, moment Mw) as if they were identical.

Keep in mind: The 1.5M + 4.8 relation is an empirical average. Real earthquakes of the same magnitude can differ in radiated energy by a factor of several, and damage depends far more on depth, distance, soil and building quality than on energy alone.

Frequently asked questions

How much stronger is a magnitude 6.5 than 6.0?

The amplitude is 10^0.5 ≈ 3.2 times larger and the energy about 10^0.75 ≈ 5.6 times larger.

Why does the energy compare to a nuclear explosion?

TNT equivalent is just a familiar energy unit; an earthquake releases its energy over a large fault and over seconds to minutes.

Which magnitude do news agencies report today?

Most seismological agencies, including the USGS, report moment magnitude (Mw) for moderate and large earthquakes, because it does not saturate for very large events.

Sources: B. Gutenberg and C. F. Richter (1956), "Magnitude and energy of earthquakes", Annali di Geofisica 9, 1–15 · U.S. Geological Survey, Earthquake Hazards Program, earthquake magnitude and energy explanations

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

Your numbers