Richter Magnitude
Earthquake magnitude from seismograph amplitude.
Formula
Variables
Example
Each whole step up the Richter scale means 10× larger ground motion.
How it works
The Richter magnitude compares the size of an earthquake’s recorded seismic wave to a standard reference level. Because the scale is logarithmic, equal jumps in magnitude represent multiplicative increases in wave amplitude rather than equal additive changes. This is useful because earthquake recordings can vary over many orders of magnitude, so a log scale compresses the range into manageable numbers while preserving relative strength.
When to use it
Use this formula when you know the amplitude measured on a seismograph and the corresponding reference amplitude for the same recording setup. It is commonly used in earth science problems to compare earthquake sizes from seismic data.
Worked example, step by step
Given: A = 5.0 mm, A0 = 0.0005 mm Step 1: Form the ratio A/A0 = 5.0 / 0.0005 = 10000 Step 2: Apply the base-10 logarithm: M = log10(10000) Step 3: Evaluate the logarithm: M = 4 Final answer: The Richter magnitude is 4.0
Common mistakes to avoid
- Using the wrong logarithm base instead of base 10
- Forgetting that A and A0 must be in the same units
- Treating magnitude as a direct linear measure rather than a logarithmic one
Did You Know?
The Richter scale is logarithmic — each whole step is 10× the shaking and about 32× the energy released.
Share this formula
More in Geography & Earth
View allHaversine Distance
AdvancedGreat-circle distance between two lat/long points.
Map Scale
BasicRatio of map distance to real-world distance.
Slope / Gradient
BasicSteepness of terrain as a percentage.
Earth Curvature Drop
AdvancedApproximate drop of the horizon over distance d.
Barometric Formula
AdvancedAtmospheric pressure as a function of altitude.
Degrees to Distance
BasicApproximate ground distance per degree of latitude.