{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"earthquake-magnitude"},"result":{"entity_type":"calculator","id":"earthquake-magnitude","calculator_id":"earthquake-magnitude","canonical_url":"https://tttkmbb.com/science/earthquake-magnitude","name":"Earthquake Magnitude Energy Calculator","title":"Earthquake Magnitude Calculator – Energy Release in Joules and TNT, Magnitude Comparison and USGS Class","category":"science","category_name":"Biology, Earth & Space","tool_name":"compare_earthquake_magnitudes","featured_mcp_tool":false,"description":"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.","use_when":"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.","inputs":[{"name":"magnitude","label":"Magnitude","type":"number","required":true,"min":-3,"max":12,"description":"Moment magnitude Mw (the Richter-type local magnitude ML is similar below about 6.5).","example":7},{"name":"compare_magnitude","label":"Compare with magnitude","type":"number","required":false,"min":-3,"max":12,"description":"Optional second magnitude for amplitude and energy ratios.","example":5}],"outputs":[{"name":"energy_joules","label":"Seismic energy","type":"number","unit":"J","decimals":0,"description":"E = 10^(1.5 M + 4.8) joules (radiated seismic energy)."},{"name":"energy_tnt_tons","label":"TNT equivalent","type":"number","unit":"t TNT","decimals":0,"description":"E / 4.184 × 10⁹ J per ton of TNT."},{"name":"energy_tnt_kilotons","label":"TNT equivalent (kt)","type":"number","unit":"kt TNT","decimals":3,"description":"Tons of TNT / 1,000."},{"name":"energy_tnt_megatons","label":"TNT equivalent (Mt)","type":"number","unit":"Mt TNT","decimals":4,"description":"Tons of TNT / 1,000,000."},{"name":"hiroshima_equivalents","label":"Hiroshima-bomb equivalents (approx.)","type":"number","decimals":2,"description":"Kilotons / 15 (the Hiroshima bomb yield is estimated at about 15 kt)."},{"name":"description","label":"USGS magnitude class","type":"string","decimals":4,"description":"Micro (< 3), Minor (3–3.9), Light (4–4.9), Moderate (5–5.9), Strong (6–6.9), Major (7–7.9) or Great (≥ 8)."},{"name":"amplitude_ratio","label":"Amplitude ratio","type":"number","decimals":4,"description":"10^(magnitude − compare_magnitude): ratio of seismic-wave amplitudes (when compare_magnitude is given)."},{"name":"energy_ratio","label":"Energy ratio","type":"number","decimals":4,"description":"10^(1.5 × (magnitude − compare_magnitude)): ratio of released energies."},{"name":"comparison","label":"Comparison","type":"string","decimals":4,"description":"Sentence comparing the two magnitudes."}],"input_schema":{"type":"object","properties":{"magnitude":{"description":"Moment magnitude Mw (the Richter-type local magnitude ML is similar below about 6.5).","type":"number","minimum":-3,"maximum":12,"examples":[7]},"compare_magnitude":{"description":"Optional second magnitude for amplitude and energy ratios.","type":"number","minimum":-3,"maximum":12,"examples":[5]}},"additionalProperties":false,"required":["magnitude"]},"output_schema":{"type":"object","properties":{"energy_joules":{"description":"E = 10^(1.5 M + 4.8) joules (radiated seismic energy). Unit: J.","type":"number","x-unit":"J"},"energy_tnt_tons":{"description":"E / 4.184 × 10⁹ J per ton of TNT. Unit: t TNT.","type":"number","x-unit":"t TNT"},"energy_tnt_kilotons":{"description":"Tons of TNT / 1,000. Unit: kt TNT.","type":"number","x-unit":"kt TNT"},"energy_tnt_megatons":{"description":"Tons of TNT / 1,000,000. Unit: Mt TNT.","type":"number","x-unit":"Mt TNT"},"hiroshima_equivalents":{"description":"Kilotons / 15 (the Hiroshima bomb yield is estimated at about 15 kt).","type":"number"},"description":{"description":"Micro (< 3), Minor (3–3.9), Light (4–4.9), Moderate (5–5.9), Strong (6–6.9), Major (7–7.9) or Great (≥ 8).","type":"string"},"amplitude_ratio":{"description":"10^(magnitude − compare_magnitude): ratio of seismic-wave amplitudes (when compare_magnitude is given).","type":"number"},"energy_ratio":{"description":"10^(1.5 × (magnitude − compare_magnitude)): ratio of released energies.","type":"number"},"comparison":{"description":"Sentence comparing the two magnitudes.","type":"string"}}},"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","method":"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.","sources":[{"name":"USGS – Earthquake Magnitude, Energy Release, and Shaking Intensity","url":"https://www.usgs.gov/programs/earthquake-hazards/earthquake-magnitude-energy-release-and-shaking-intensity","type":"government","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Moment magnitude scale","url":"https://en.wikipedia.org/wiki/Moment_magnitude_scale","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Magnitude 7 compared with magnitude 5","inputs":{"magnitude":7,"compare_magnitude":5},"expected":{"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},"url":"https://tttkmbb.com/api/v1/calculate/earthquake-magnitude?magnitude=7&compare_magnitude=5"},{"name":"Magnitude 9.1 (2011 Tōhoku)","inputs":{"magnitude":9.1},"expected":{"energy_joules":2818000000000000000,"energy_tnt_megatons":673.61,"hiroshima_equivalents":44907,"description":"Great (8.0 and higher)"},"url":"https://tttkmbb.com/api/v1/calculate/earthquake-magnitude?magnitude=9.1"}],"faq":[{"q":"Is the energy the total energy of the earthquake?","a":"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."},{"q":"Why is one magnitude step 31.6 times the energy but 10 times the amplitude?","a":"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."},{"q":"Which magnitude scale should I enter?","a":"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."}],"tags":["earthquake magnitude","seismic energy","richter scale","moment magnitude","tnt equivalent","magnitude comparison"],"related":[{"calculator_id":"logarithm","reason":"The base-10 logarithm behind the magnitude scale."},{"calculator_id":"energy","reason":"Convert joules to other energy units."},{"calculator_id":"kinetic-energy","reason":"Compare with the kinetic energy of moving objects."}],"links":{"html":"https://tttkmbb.com/science/earthquake-magnitude","markdown":"https://tttkmbb.com/science/earthquake-magnitude.md","json":"https://tttkmbb.com/science/earthquake-magnitude.json","api":"https://tttkmbb.com/api/v1/calculate/earthquake-magnitude","schema":"https://tttkmbb.com/api/v1/calculators/earthquake-magnitude","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:51:43Z","next_actions":[{"tool":"run_calculator","calculator_id":"earthquake-magnitude","reason":"Run Earthquake Magnitude Energy Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/science/earthquake-magnitude.md"}}