Richter Magnitude Calculator

Estimate an earthquake's local (Richter) magnitude from the maximum recorded seismogram amplitude and the epicentral distance to the station.

🌍 Richter Magnitude Calculator
Maximum amplitude (A)1 mm
mm
0.0150
Epicentral distance (D)100 km
km
1500
Local magnitude (ML)
—
Step-by-step working

🌍 What is the Richter Magnitude Scale?

Local magnitude (ML), popularly known as the Richter scale, is a logarithmic measure of earthquake size introduced by Charles Richter in 1935. It estimates magnitude from the maximum amplitude recorded on a seismogram, corrected for the distance between the earthquake and the recording station, using a formula approximating ML = log10(A) + 2.56*log10(D) - 1.67.

Seismologists and earthquake-preparedness planners use magnitude estimates like this to quickly classify earthquake size from a single station's recording, compare relative earthquake sizes across a seismic catalog, communicate hazard levels to the public, and understand why doubling the recorded shaking amplitude doesn't mean "twice as strong" on a linear scale, since the scale itself is logarithmic.

A common point of confusion is treating "Richter magnitude" and "moment magnitude" as interchangeable. They are similar for moderate earthquakes but diverge for large ones, local magnitude saturates (loses accuracy) above roughly magnitude 6.5 to 7, which is why modern seismology primarily reports moment magnitude for major earthquakes, even though media often still call it "the Richter scale."

This calculator estimates local magnitude from your maximum recorded amplitude and epicentral distance, and plots how the same recorded amplitude implies increasingly larger true magnitude as distance grows, since seismic waves attenuate over distance.

📐 Formula

ML = log10(A) + 2.56×log10(D) − 1.67
A = maximum seismogram amplitude (mm, Wood-Anderson equivalent)
D = epicentral distance from source to station (km)
Example: A = 1 mm, D = 100 km → ML = 3.45.

📖 How to Use This Calculator

Steps

1
Enter the maximum seismogram amplitude. Type the maximum trace amplitude in millimeters, as would be measured on a Wood-Anderson seismograph.
2
Enter the epicentral distance. Type the distance from the earthquake's epicenter to the recording station, in kilometers.
3
Read the estimated local magnitude. The calculator applies the attenuation-corrected formula to report the estimated local (Richter) magnitude.

💡 Example Calculations

Example 1 — Moderate Local Earthquake

A = 1 mm, D = 100 km

1
ML = log10(1) + 2.56×log10(100) − 1.67 = 0 + 5.12 − 1.67
ML = 3.45
Try this example →

Example 2 — Small Nearby Earthquake

A = 0.1 mm, D = 50 km

1
ML = log10(0.1) + 2.56×log10(50) − 1.67 = -1 + 4.349 − 1.67
ML = 1.68
Try this example →

Example 3 — Larger, More Distant Earthquake

A = 10 mm, D = 200 km

1
ML = log10(10) + 2.56×log10(200) − 1.67 = 1 + 5.891 − 1.67
ML = 5.22
Try this example →

❓ Frequently Asked Questions

What is the Richter magnitude scale?+
The Richter magnitude scale (formally local magnitude, ML) is a logarithmic measure of earthquake size introduced by Charles Richter in 1935, based on the maximum amplitude recorded on a Wood-Anderson seismograph, corrected for the distance between the earthquake and the recording station.
What is the formula for local (Richter) magnitude?+
A common simplified approximation is ML = log10(A) + 2.56*log10(D) - 1.67, where A is the maximum trace amplitude in millimeters on a Wood-Anderson seismograph and D is the epicentral distance in kilometers. This approximates Richter's original empirically-derived attenuation correction.
Why does the formula add a term for distance?+
Seismic wave amplitude decreases (attenuates) as it travels farther from the earthquake source. A station recording a given amplitude at a greater distance must have been shaken by a proportionally larger earthquake than a station recording the same amplitude nearby, so the distance term corrects for this attenuation.
Is the Richter scale the same as the moment magnitude scale?+
No, though they are numerically similar for moderate earthquakes and often confused in casual usage. Local magnitude (Richter) is based on a single seismogram's amplitude and saturates (stops increasing accurately) above roughly magnitude 6.5 to 7, while moment magnitude (Mw) is based on the physical seismic moment and remains accurate for the largest earthquakes.
How much stronger is a magnitude 6 earthquake than a magnitude 5?+
About 10 times greater ground motion amplitude, since the scale is base-10 logarithmic. In terms of released energy (which scales differently, roughly as amplitude to the 1.5 power), a one-magnitude increase corresponds to about 31.6 times more energy release.
What is a Wood-Anderson seismograph?+
It's the specific torsion seismograph instrument Richter used to define his original local magnitude scale in 1935. Modern seismic networks use different instruments but apply calibrated conversion factors to report magnitudes on the same historical Richter scale.
Does this calculator work for any earthquake distance and size?+
This calculator uses a simplified approximation intended for typical local-to-regional distances (tens to a few hundred kilometers) and moderate magnitudes, matching the original scale's calibration range. Very large, very distant, or deep-focus earthquakes require more sophisticated magnitude scales and corrections.
Why do earthquake magnitudes sometimes get revised after initial reports?+
Initial magnitude estimates often come from a small number of nearby stations using fast automated methods. As more station data and different magnitude scales (like moment magnitude) are incorporated over hours to days, agencies typically revise the figure to a more accurate final value.
What is the smallest earthquake magnitude this scale can measure?+
The scale has no strict lower bound, modern sensitive instruments regularly detect and assign negative or near-zero local magnitudes to very small earthquakes imperceptible to humans, though the scale is most commonly discussed for magnitude 2 and above (the typical threshold of human perceptibility).
What units does this calculator use?+
Maximum seismogram amplitude is entered in millimeters (as traced on a Wood-Anderson-equivalent instrument) and epicentral distance in kilometers. The result, local magnitude, is a dimensionless number on the standard Richter scale.
Tags: Richter Magnitude Calculator Richter Scale Calculator Local Magnitude Calculator Earthquake Magnitude Calculator Seismic Magnitude Calculator Calculator Formula Free Online

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What is the Richter magnitude scale?

The Richter magnitude scale (formally local magnitude, ML) is a logarithmic measure of earthquake size introduced by Charles Richter in 1935, based on the maximum amplitude recorded on a Wood-Anderson seismograph, corrected for the distance between the earthquake and the recording station.

What is the formula for local (Richter) magnitude?

A common simplified approximation is ML = log10(A) + 2.56*log10(D) - 1.67, where A is the maximum trace amplitude in millimeters on a Wood-Anderson seismograph and D is the epicentral distance in kilometers. This approximates Richter's original empirically-derived attenuation correction.

Why does the formula add a term for distance?

Seismic wave amplitude decreases (attenuates) as it travels farther from the earthquake source. A station recording a given amplitude at a greater distance must have been shaken by a proportionally larger earthquake than a station recording the same amplitude nearby, so the distance term corrects for this attenuation.

Is the Richter scale the same as the moment magnitude scale?

No, though they are numerically similar for moderate earthquakes and often confused in casual usage. Local magnitude (Richter) is based on a single seismogram's amplitude and saturates (stops increasing accurately) above roughly magnitude 6.5 to 7, while moment magnitude (Mw) is based on the physical seismic moment and remains accurate for the largest earthquakes.

How much stronger is a magnitude 6 earthquake than a magnitude 5?

About 10 times greater ground motion amplitude, since the scale is base-10 logarithmic. In terms of released energy (which scales differently, roughly as amplitude to the 1.5 power), a one-magnitude increase corresponds to about 31.6 times more energy release.

What is a Wood-Anderson seismograph?

It's the specific torsion seismograph instrument Richter used to define his original local magnitude scale in 1935. Modern seismic networks use different instruments but apply calibrated conversion factors to report magnitudes on the same historical Richter scale.

Does this calculator work for any earthquake distance and size?

This calculator uses a simplified approximation intended for typical local-to-regional distances (tens to a few hundred kilometers) and moderate magnitudes, matching the original scale's calibration range. Very large, very distant, or deep-focus earthquakes require more sophisticated magnitude scales and corrections.

Why do earthquake magnitudes sometimes get revised after initial reports?

Initial magnitude estimates often come from a small number of nearby stations using fast automated methods. As more station data and different magnitude scales (like moment magnitude) are incorporated over hours to days, agencies typically revise the figure to a more accurate final value.

What is the smallest earthquake magnitude this scale can measure?

The scale has no strict lower bound, modern sensitive instruments regularly detect and assign negative or near-zero local magnitudes to very small earthquakes imperceptible to humans, though the scale is most commonly discussed for magnitude 2 and above (the typical threshold of human perceptibility).

What units does this calculator use?

Maximum seismogram amplitude is entered in millimeters (as traced on a Wood-Anderson-equivalent instrument) and epicentral distance in kilometers. The result, local magnitude, is a dimensionless number on the standard Richter scale.

📌 Quick Tips

💡The Richter (local magnitude, ML) scale is logarithmic, each whole-number increase represents roughly a 10x increase in recorded amplitude and about 31.6x more released energy, a magnitude 6 earthquake is not 'a bit stronger' than a magnitude 5, it is dramatically stronger.
💡For the same recorded amplitude, a station farther from the epicenter implies a larger true earthquake magnitude, since seismic waves attenuate (lose amplitude) with distance, this is exactly why the distance term enters positively in the formula.
💡Richter's original local magnitude scale was calibrated for shallow Southern California earthquakes recorded on a specific instrument (the Wood-Anderson seismograph) at distances up to a few hundred kilometers, it saturates and becomes unreliable for very large or very distant earthquakes.
💡Modern seismology primarily uses moment magnitude (Mw) for large earthquakes, since it doesn't saturate the way local magnitude does at high values, media reports of 'Richter scale' readings today are often actually moment magnitude.
💡This calculator uses a standard simplified approximation to Richter's original empirically-tabulated attenuation curve, real seismological practice uses station-specific calibration tables or software for higher precision.