Richter Scale Energy Calculator
ANA›Life Services Authority›National Calculator Authority›Richter Scale Energy Calculator
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Richter Scale Energy Calculator
Calculate the seismic energy released by an earthquake based on its Richter Scale (local magnitude) value.
Richter Magnitude (M)
M
Calculate Enter a magnitude to see results.
function ricCalc() { const resultDiv = document.getElementById('ric-result'); const magInput = document.getElementById('ric-magnitude'); const M = parseFloat(magInput.value);
// --- Validation --- if (magInput.value.trim() === '') { resultDiv.innerHTML = 'Please enter a magnitude value.'; return; } if (isNaN(M)) { resultDiv.innerHTML = 'Magnitude must be a valid number.'; return; } if (M 10) { resultDiv.innerHTML = 'Magnitude must be between -2 and 10.'; return; }
// --- Formula --- // Gutenberg–Richter energy formula: // log10(E) = 11.8 + 1.5 * M (E in ergs) // Source: Gutenberg & Richter (1956) const log10E = 11.8 + 1.5 * M; const E_ergs = Math.pow(10, log10E); // energy in ergs const E_joules = E_ergs * 1e-7; // 1 erg = 1e-7 joules const E_tnt = E_joules / 4.184e9; // 1 ton TNT = 4.184e9 J → result in kilotons const E_tnt_kt = E_tnt; // already in kilotons of TNT
// Comparison multiplier relative to M 1.0 earthquake const log10E_ref = 11.8 + 1.5 * 1.0; const E_ref = Math.pow(10, log10E_ref); const ratio = E_ergs / E_ref;
// Energy step between whole magnitudes const stepFactor = Math.pow(10, 1.5).toFixed(2); // ~31.62
// Format helpers function fmtSci(val) { if (val === 0) return '0'; const exp = Math.floor(Math.log10(Math.abs(val))); const coeff = (val / Math.pow(10, exp)).toFixed(3); return coeff + ' × 10' + exp + ''; } function fmtNum(val) { if (val >= 1e12) return (val/1e12).toFixed(3) + ' trillion'; if (val >= 1e9) return (val/1e9).toFixed(3) + ' billion'; if (val >= 1e6) return (val/1e6).toFixed(3) + ' million'; if (val >= 1e3) return (val/1e3).toFixed(3) + ' thousand'; return val.toFixed(4); }
// Qualitative description let desc = ''; if (M ' + 'ParameterValue' + 'log10(E)' + log10E.toFixed(4) + '' + 'Energy (ergs)' + fmtSci(E_ergs) + ' ergs' + 'Energy (joules)' + fmtSci(E_joules) + ' J' + 'Energy (kilotons TNT)' + fmtSci(E_tnt_kt) + ' kt TNT' + 'Ratio vs M 1.0' + fmtNum(ratio) + '×' + 'Classification' + desc + '' + '' + 'Each 1-unit increase in magnitude releases ~' + stepFactor + '× more energy.
'; }
#### Formula
The Gutenberg–Richter (1956) empirical relation between seismic energy and magnitude:
log10(E) = 11.8 + 1.5 × M
where E is energy in ergs and M is the Richter (local) magnitude.
Unit conversions applied:
- 1 erg = 10−7 joules
- 1 kiloton TNT = 4.184 × 1012 joules
Each whole-number increase in magnitude corresponds to a 101.5 ≈ 31.62× increase in energy released.
#### Assumptions & References
- Formula is valid for the Richter local magnitude scale (ML); results are approximate for moment magnitude (Mw).
- The relationship is empirical and represents total seismic wave energy, not surface destruction energy.
- Gutenberg, B. & Richter, C.F. (1956) – "Earthquake magnitude, intensity, energy, and acceleration." Bulletin of the Seismological Society of America, 46(2), 105–145.
- USGS Earthquake Hazards Program – usgs.gov
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