Earthquake Magnitude Calculator

Four modes covering magnitude scales, seismic energy comparisons, Modified Mercalli Intensity (I-XII), and Richter magnitude from seismograph amplitude. Presets include historic earthquakes.

Seismograph Waveform

Waveform amplitude is proportional to magnitude. Higher M = larger displacement.

Controls

Mode

Presets

Magnitude (M)6.0

0510

Seismic Moment M₀ (N·m)

Try: 1e18 (M6), 1e20 (M7), 3.9e22 (M9.1 Japan)

Results

Magnitude

6.0

Strong — structural damage

Seismic Energy

63.10 TJ

(6.31e+13 J)

TNT Equivalent

15.08 kt TNT

1.0 atomic bombs

\log_{10}(E) = 1.5M + 4.8 \Rightarrow E \approx 6.31e+13 \text{ J}

Moment Magnitude M𝑤

M_w = \tfrac{2}{3}\log_{10}(M_0) - 10.7

1.30

Modified Mercalli Intensity

VIII

Severe

Level 8 of 12

Richter Mₗ from Amplitude

Mₗ = 4.00

M_L = \log_{10}(A) + \log_{10}(\Delta/100) + 3

Energy Comparison (Log Scale)

Each magnitude step = 31.6× more energy. Two steps = 1,000×.

Key fact: The 2011 Japan M9.1 earthquake released about 600× more energy than the 1906 San Francisco M7.9. That is 10^(1.5 × 1.2) ≈ 63× per step times ~10 steps difference.

Modified Mercalli Intensity Scale (I-XII)

Not felt~M < 2.0

Not felt except by a very few under especially favorable conditions.

Weak~M 2.0 - 2.9

Felt only by a few persons at rest, especially on upper floors. Delicately suspended objects may swing.

III

Weak~M 2.0 - 2.9

Felt quite noticeably by persons indoors. Many do not recognize it as an earthquake. Vibration like a passing truck.

Light~M 3.0 - 3.9

Felt indoors by many. Dishes, windows, and doors disturbed. Walls make cracking sound.

Moderate~M 4.0 - 4.9

Felt by nearly everyone. Some dishes and windows broken. Unstable objects overturned.

Strong~M 4.0 - 4.9

Felt by all. Some heavy furniture moved. A few instances of fallen plaster. Damage slight.

VII

Very Strong~M 5.0 - 5.9

Damage negligible in well-built structures. Considerable damage in poor structures. Some chimneys broken.

VIII

Severe~M 5.0 - 5.9

Damage slight in specially designed structures. Considerable damage in ordinary buildings with partial collapse. Panel walls thrown out of frame structures.

Violent~M 6.0 - 6.9

Damage considerable in specially designed structures. Well-designed frame structures thrown out of plumb. Ground cracked conspicuously.

Extreme~M 6.0 - 6.9

Some well-built wooden structures destroyed. Most masonry and frame structures destroyed. Rails bent. Landslides considerable.

Extreme~M 7.0+

Few if any masonry structures remain standing. Bridges destroyed. Broad fissures in ground.

XII

Extreme~M 8.0+

Damage total. Lines of sight and level are distorted. Objects thrown into the air.

Reference Guide

Richter Scale (Mₗ)

The Richter scale (local magnitude Mₗ) was developed by Charles Richter in 1935. It measures the maximum amplitude recorded by a Wood-Anderson seismometer at 100 km from the epicenter.

M_L = \log_{10}(A) - \log_{10}(A_0)

where A is the measured amplitude and A₀ is a reference amplitude at the same distance. Each whole number increase represents a tenfold increase in amplitude, but 31.6× more seismic energy.

M < 2.0Micro, not felt M 2.0 - 3.9Minor, felt slightly M 4.0 - 4.9Light, indoor shaking M 5.0 - 5.9Moderate, some damage M 6.0 - 6.9Strong, serious damage M 7.0+Major to great

Moment Magnitude (M𝑤)

Moment magnitude is the modern standard for measuring large earthquakes. It is derived from the seismic moment M₀ (in N·m), which captures the fault area, slip distance, and rock rigidity.

M_w = \tfrac{2}{3}\log_{10}(M_0) - 10.7

The 2011 Tohoku earthquake had a seismic moment of about 3.9 × 10^22 N·m giving M𝑤 = 9.1. Unlike the Richter scale, M𝑤 does not saturate for very large events and remains accurate above M7.

M_0 = \mu \cdot A \cdot D

μ = shear modulus (~3×10^10 Pa), A = fault area, D = average slip

Seismic Energy

The Gutenberg-Richter energy-magnitude relation converts magnitude to radiated seismic energy in joules:

\log_{10}(E) = 1.5M + 4.8

Each 1.0 magnitude increase = 10^1.5 ≈ 31.6× more energy. Two steps = 1,000×. A M9 earthquake releases about 31.6^4 ≈ one million times more energy than M5.

M5~2 TJ (car bomb) M6~63 TJ (small nuke) M7~2 PJ (large nuke) M8~63 PJ (meteor impact) M9~2 EJ (supervolcano)

Modified Mercalli Intensity

The Modified Mercalli Intensity (MMI) scale describes earthquake effects on people, structures, and the environment using Roman numerals I (not felt) through XII (total destruction). Unlike magnitude, MMI varies with distance from the epicenter.

I-III Not felt to weak indoor shaking IV-VI Felt by all, minor to moderate damage VII-IX Structural damage, ground cracking X-XII Extreme destruction, total damage

Empirical correlation: MMI ≈ 1.5M - 1.4. A M6.5 earthquake typically produces MMI VIII at the epicenter and MMI V-VI at 50 km distance.