# 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.

- Calculator id: `earthquake-magnitude` · Category: Biology, Earth & Space (`science`) · Tool name: `compare_earthquake_magnitudes`
- Canonical page: https://tttkmbb.com/science/earthquake-magnitude · This document: https://tttkmbb.com/science/earthquake-magnitude.md · JSON definition: https://tttkmbb.com/science/earthquake-magnitude.json

## Purpose

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.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `magnitude` | number |  | required | Moment magnitude Mw (the Richter-type local magnitude ML is similar below about 6.5). (min -3, max 12) |
| `compare_magnitude` | number |  | optional | Optional second magnitude for amplitude and energy ratios. (min -3, max 12) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `energy_joules` | number | J | E = 10^(1.5 M + 4.8) joules (radiated seismic energy). |
| `energy_tnt_tons` | number | t TNT | E / 4.184 × 10⁹ J per ton of TNT. |
| `energy_tnt_kilotons` | number | kt TNT | Tons of TNT / 1,000. |
| `energy_tnt_megatons` | number | Mt TNT | Tons of TNT / 1,000,000. |
| `hiroshima_equivalents` | number |  | Kilotons / 15 (the Hiroshima bomb yield is estimated at about 15 kt). |
| `description` | string |  | 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). |
| `amplitude_ratio` | number |  | 10^(magnitude − compare_magnitude): ratio of seismic-wave amplitudes (when compare_magnitude is given). |
| `energy_ratio` | number |  | 10^(1.5 × (magnitude − compare_magnitude)): ratio of released energies. |
| `comparison` | string |  | Sentence comparing the two magnitudes. |

## 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.

## Data Sources

- USGS – Earthquake Magnitude, Energy Release, and Shaking Intensity — https://www.usgs.gov/programs/earthquake-hazards/earthquake-magnitude-energy-release-and-shaking-intensity (government, retrieved 2026-09-24)
- Wikipedia – Moment magnitude scale — https://en.wikipedia.org/wiki/Moment_magnitude_scale (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/earthquake-magnitude?magnitude=…`
- `POST https://tttkmbb.com/api/v1/calculate/earthquake-magnitude` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/earthquake-magnitude · OpenAPI operationId `compare_earthquake_magnitudes` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "earthquake-magnitude", "inputs": {…}}`

## Example

- Magnitude 7 compared with magnitude 5: inputs `{"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): inputs `{"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
```

## Limitations

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. 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. All values are computed from the formula above; no measurement or live data is involved.

## 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.

## Related

- [Logarithm Calculator](https://tttkmbb.com/math/logarithm.md) — The base-10 logarithm behind the magnitude scale.
- [Energy Converter](https://tttkmbb.com/conversion/energy.md) — Convert joules to other energy units.
- [Kinetic Energy Calculator](https://tttkmbb.com/physics/kinetic-energy.md) — Compare with the kinetic energy of moving objects.