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Earthquake Magnitude Energy Calculator

Converts a moment magnitude into radiated seismic energy with the Gutenberg–Richter relation log10 E = 1.5 M + 4.8, expresses it in tons of TNT and Hiroshima-bomb equivalents, classifies the magnitude with the USGS classes and compares two magnitudes by wave amplitude and energy.

When to use

You want to know how much energy an earthquake of a given magnitude releases, how many times stronger one magnitude is than another, or which descriptive class (minor, moderate, major, great) a magnitude belongs to.

Do not use when: You need shaking intensity or damage at a location (Modified Mercalli intensity depends on distance, depth and soil), or magnitudes on other scales without conversion to moment magnitude.

Formula

log10(E_J) = 1.5 × M + 4.8; tons TNT = E / (4.184 × 10⁹); amplitude ratio = 10^(M − M₂); energy ratio = 10^(1.5 × (M − M₂)); Hiroshima equivalents = kilotons / 15

Gutenberg–Richter energy–magnitude relation as given by USGS (each whole magnitude step is 10 times the amplitude and about 31.6 times the energy). The TNT figures compare radiated seismic energy only; an explosion's total energy is mostly not radiated as seismic waves, so bomb comparisons are approximate.

Inputs

ParameterTypeUnitRequiredDescription
magnitudenumberyesMoment magnitude Mw (the Richter-type local magnitude ML is similar below about 6.5). Range: ≥ -3, ≤ 12
compare_magnitudenumbernoOptional second magnitude for amplitude and energy ratios. Range: ≥ -3, ≤ 12

Outputs

OutputTypeUnitDescription
energy_joulesnumberJE = 10^(1.5 M + 4.8) joules (radiated seismic energy).
energy_tnt_tonsnumbert TNTE / 4.184 × 10⁹ J per ton of TNT.
energy_tnt_kilotonsnumberkt TNTTons of TNT / 1,000.
energy_tnt_megatonsnumberMt TNTTons of TNT / 1,000,000.
hiroshima_equivalentsnumberKilotons / 15 (the Hiroshima bomb yield is estimated at about 15 kt).
descriptionstringMicro (< 3), Minor (3–3.9), Light (4–4.9), Moderate (5–5.9), Strong (6–6.9), Major (7–7.9) or Great (≥ 8).
amplitude_rationumber10^(magnitude − compare_magnitude): ratio of seismic-wave amplitudes (when compare_magnitude is given).
energy_rationumber10^(1.5 × (magnitude − compare_magnitude)): ratio of released energies.
comparisonstringSentence comparing the two magnitudes.

Example

Magnitude 7 compared with magnitude 5: {"magnitude":7,"compare_magnitude":5} → {"energy_joules":1995000000000000,"energy_tnt_tons":476879,"energy_tnt_megatons":0.4769,"hiroshima_equivalents":31.79,"description":"Major (7.0–7.9)","amplitude_ratio":100,"energy_ratio":1000}

Magnitude 9.1 (2011 Tōhoku): {"magnitude":9.1} → {"energy_joules":2818000000000000000,"energy_tnt_megatons":673.61,"hiroshima_equivalents":44907,"description":"Great (8.0 and higher)"}

GET https://tttkmbb.com/api/v1/calculate/earthquake-magnitude?magnitude=7&compare_magnitude=5

Machine access

Sources

FAQ

Is the energy the total energy of the earthquake?

No, it is the radiated seismic energy estimated from magnitude; the total energy (including heat and rock fracture) is larger and is not well constrained by magnitude alone.

Why is one magnitude step 31.6 times the energy but 10 times the amplitude?

Magnitude is defined on wave amplitude (base-10 logarithm), while radiated energy scales with 10^(1.5 M), so ΔM = 1 gives 10^1.5 ≈ 31.6 times the energy and ΔM = 2 gives 1,000 times.

Which magnitude scale should I enter?

Moment magnitude (Mw), the scale used for modern reporting; the formula was calibrated on surface-wave magnitude and moment magnitude is designed to match it. Local magnitude (ML) saturates above about 6.5.

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