Richter Magnitude Scale Calculator
Calculate local earthquake magnitude from seismograph amplitude readings, or work backward to find amplitude from a known magnitude. Built for geology and earth-science students, and anyone learning how the Richter scale works.
Enter your amplitude readings
Magnitude = log₁₀ of the recorded amplitude divided by a reference amplitude.
Advanced calculation
Choose what you need to solve for, then fill in the two known values.
Result
Your calculation steps and interpretation will appear here.
Enter values on the left and click Calculate to see the magnitude, the formula used, and what the number means.
Magnitude Classification
General educational guidance only — actual effects at a given magnitude vary widely with depth, distance, local geology, and building construction. This table is not a damage predictor for any specific earthquake.
| Magnitude | Class | Typically observed as |
|---|---|---|
| < 2.0 | Micro | Not felt; recorded only by sensitive instruments. |
| 2.0 – 3.9 | Minor | Often felt nearby; rarely causes damage. |
| 4.0 – 4.9 | Light | Noticeable shaking; damage is unlikely to be significant. |
| 5.0 – 5.9 | Moderate | Can cause damage to poorly built structures. |
| 6.0 – 6.9 | Strong | Can be destructive in populated areas. |
| 7.0 – 7.9 | Major | Serious damage over larger areas. |
| ≥ 8.0 | Great | Serious damage across very large regions. |
Practical Examples
1. Basic student example
A₀ = 0.001 mm
M = log₁₀(1000) = 3.00
An amplitude 1,000 times the reference gives a magnitude of exactly 3 — each whole number step is a 10× jump in amplitude.
2. Moderate earthquake example
A₀ = 0.001 mm
M = log₁₀(10000) = 4.00
A 10 mm trace against the standard reference works out to a light-magnitude event.
3. Reverse calculation
A = A₀ × 10^M
A = 0.001 × 10⁵ = 100 mm
Given a target magnitude and the reference amplitude, the trace amplitude that would produce it is solved directly.
4. Comparing two magnitudes
Amplitude ratio = 10^(M₁−M₂) = 100×
Energy ratio ≈ 10^(1.5×2) ≈ 1,000×
Every whole magnitude step is 10 times the amplitude but roughly 31.6 times the energy — two steps compound to about 1,000 times the energy.
What Is Richter Magnitude?
The Richter local magnitude (ML) scale, introduced by Charles Richter in 1935, measures earthquake size from the maximum amplitude recorded on a seismogram, compared against a reference amplitude for a "zero magnitude" event on the same type of instrument at a standard distance. Because M = log₁₀(A/A₀), the scale is logarithmic: each whole-number increase represents a tenfold increase in recorded amplitude.
Amplitude vs. energy
A 10× jump in amplitude corresponds to roughly a 31.6× jump in radiated energy (from the Gutenberg–Richter energy relation, log₁₀E ≈ 1.5M + 4.8). That's why a magnitude 7 earthquake releases far more than "twice" the energy of a magnitude 6 — it's closer to 31 times as much.
Limits of this calculator
Real seismic practice corrects A₀ for epicentral distance using empirical tables, and modern agencies generally report moment magnitude (Mw) rather than ML for larger or more distant events, since ML tends to saturate above roughly magnitude 6–7.
This tool applies the plain M = log₁₀(A/A₀) formula with whatever A₀ you supply — it does not apply distance corrections or convert between magnitude scales.
How to Use This Tool
Select Basic Mode for a straightforward M = log₁₀(A/A₀) calculation, or Advanced Mode for reverse calculations and magnitude comparisons.
Enter the recorded amplitude (A) — the maximum trace deflection measured on the seismogram.
Enter the reference amplitude (A₀), or use the standard 0.001 mm shortcut if that fits your reading.
Choose the correct units for each amplitude — the tool converts between mm, μm, cm, and m automatically.
Click Calculate Magnitude.
Review the calculated magnitude, the step-by-step working, and the classification below it.
Switch to Advanced Mode when you need to solve for A or A₀ instead, or want to compare two magnitudes.
What This Tool Offers
Formula Reference
Recent Calculations
Stored only in this browser — never sent to a server.
| Time | A | A₀ | Magnitude |
|---|
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| M | Magnitude | |
| A | Measured wave amplitude | |
| A₀ | Reference amplitude |
What it means
The Richter magnitude scale was developed by Charles Richter in 1935 to quantify the size of earthquakes. It is a logarithmic scale based on the amplitude of seismic waves recorded on a seismograph at a standard distance. The formula relates the measured amplitude A to a reference amplitude A₀. A magnitude increase of 1 corresponds to a tenfold increase in wave amplitude and approximately 31.6 times more energy release. Although superseded by the Moment Magnitude scale (Mw) for larger earthquakes, the Richter scale is still used for smaller events. It is fundamental in seismology for comparing earthquake sizes and for assessing potential damage. Understanding this scale is essential for geologists, civil engineers, and emergency planners to evaluate seismic hazards and to design resilient structures.
Worked example
Richter Magnitude Scale – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| A (mm) | 100 |
| A₀ (mm) | 1 |
| Parameter | Value |
|---|---|
| A | 316 |
| A₀ | 1 |
Common mistakes
- Logarithm base: Uses base‑10 logarithm (log₁₀) – not natural log.
- Amplitude ratio: The formula subtracts log(A₀) where A₀ is a reference amplitude (usually 0.001 mm at 100 km).
- Distance correction: Different scales (local, body, surface waves) use different calibration – not all magnitudes are directly comparable.
- Saturation: Richter scale saturates for large earthquakes (M > 7) – use moment magnitude for large events.
- Instrumentation: Different seismometers may give different amplitudes – use calibrated instruments.
Applications
The Richter magnitude scale, M = log₁₀(A) − log₁₀(A₀), was one of the first quantitative measures of earthquake size, based on the logarithm of the maximum amplitude (A) recorded on a seismograph, referenced to a standard amplitude (A₀) at a specific distance. Although now superseded by the moment magnitude scale for large events, it remains a familiar concept for communicating earthquake size to the public. Seismologists use it to quickly estimate event magnitude for smaller regional earthquakes. It also laid the groundwork for understanding the energy released during seismic events. By calculating magnitude, scientists can assess the potential for damage, issue warnings, and study earthquake statistics. The logarithmic nature means each whole number step represents a tenfold increase in amplitude and about 31.6 times more energy release. Understanding the Richter scale is essential for basic seismology and public education.
- Rapid estimation of earthquake size for regional events
- Public communication of earthquake severity
- Seismic hazard assessment and statistical analysis
- Educational introduction to earthquake magnitude scales
- Historical comparison of earthquakes recorded on seismographs
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