Amplitude ratios and earthquake magnitude scales
Earthquake magnitude scales are logarithmic. A difference of one magnitude unit corresponds to a factor of ten in the amplitude measure used by the applicable scale, after its specified processing and corrections.
This calculator only evaluates log₁₀ of a measured-to-reference amplitude ratio. Local magnitude requires calibrated seismograms and distance corrections; moment magnitude is derived from seismic moment. The output must not be reported as an earthquake’s magnitude.
How to use the earthquake amplitude-ratio calculator
- Enter measured amplitude: Provide a positive waveform amplitude.
- Enter reference amplitude: Use a positive value in exactly the same unit and measurement convention.
- Calculate the ratio index: Interpret the result as a logarithmic amplitude comparison only.
- Use authoritative event magnitudes: For real earthquakes, consult a seismic network such as USGS rather than this educational calculation.
Formula and variables
This relationship compares two positive amplitudes measured consistently. Operational scale formulas include additional definitions and corrections.
ΔM = log₁₀(A/A₀)- A — Measured amplitude
- Positive amplitude under a consistent measurement convention
- A₀ — Reference amplitude
- Positive baseline amplitude in the same unit
- ΔM — Log amplitude ratio
- Base-10 logarithm of the amplitude ratio
Thousandfold amplitude ratio
Compare an amplitude of 1,000 with a same-unit reference amplitude of 1.
- A
- 1,000
- A₀
- 1
- ΔM = log₁₀(1,000/1)
- ΔM = log₁₀(10³)
Result: The log amplitude ratio is 3.
This illustrates a three-unit amplitude-scale difference but does not determine an event magnitude.
Understanding your results
Do not label the result Richter magnitude
Recorded amplitude depends strongly on distance, instrument response, frequency band, propagation path, and site conditions.
- A result of 1 means a tenfold amplitude ratio.
- A result of 2 means a hundredfold amplitude ratio.
- Energy ratios do not follow the same factor as amplitude ratios.
- Modern authoritative reporting commonly uses moment magnitude for larger events.
Assumptions
- Both amplitudes are positive and use identical units.
- The comparison uses a base-10 logarithm.
- The result is interpreted only as an amplitude-ratio index.
Limitations
- Does not calculate local, body-wave, surface-wave, duration, or moment magnitude.
- Does not include epicentral distance, attenuation, depth, instrument response, waveform period, station corrections, or network averaging.
- Must not be used for hazard decisions or reporting earthquake size.
Common mistakes
- Calling the raw ratio result Richter magnitude.
- Comparing amplitudes from different instruments or units.
- Ignoring source-to-station distance.
- Assuming a tenfold amplitude increase means tenfold energy release.
Practical use cases
Logarithmic-scale education
Demonstrate how amplitude ratios translate into base-10 magnitude differences.
Amplitude comparison
Compare two consistently defined positive amplitudes without claiming an event magnitude.
Frequently asked questions
Does this calculate Richter magnitude?
No. Local magnitude requires calibrated instrument amplitude plus a distance-dependent correction.
Why do real earthquakes have one reported magnitude but different shaking?
Magnitude estimates source size; local shaking intensity varies with distance, geology, depth, and other conditions.
What magnitude scale does USGS commonly use?
Moment magnitude is generally preferred for larger earthquakes, while several scale types are used depending on available data and event size.
Sources and review
- Earthquake Magnitude, Energy Release, and Shaking Intensity — U.S. Geological Survey. Accessed 2026-07-13.
- Magnitude Types — U.S. Geological Survey. Accessed 2026-07-13.
Reviewed 2026-07-13.