Earthquakes range from tiny tremors no one feels to giants that shake whole countries. Magnitude measures an earthquake's size with one number. Each step up is a big jump, because the scale uses powers of 10.
Key idea
Each whole step up in magnitude means seismic waves about 10 times taller on a seismogram and about 32 times more energy released. Two steps means 100 times taller waves and about 1,000 times the energy.
Why it works
Quake sizes span a huge range, so seismologists use a scale that counts powers of ten, the way an exponent does. Going from magnitude 4 to 6 is two steps: waves $10 \times 10 = 10^2 = 100$ times taller, and energy about $32 \times 32 \approx 1{,}000$ times more. Today the U.S. Geological Survey uses the moment magnitude scale, built from the size of the fault break and how far it slipped, but the steps work the same way.
| Magnitude change | Wave height (amplitude) | Energy |
|---|---|---|
| +1 | × 10 | about × 32 |
| +2 | × 100 | about × 1,000 |
| +3 | × 1,000 | about × 32,000 |
Worked example: How much taller?
A magnitude 6 earthquake and a magnitude 4 earthquake are recorded the same distance away. How many times taller are the bigger one's waves?
- The difference is $6 - 4 = 2$ steps.
- Each step is × 10: $10^2 = 100$ times taller.
Answer: 100 times
Worked example: Energy
About how many times more energy does a magnitude 7 release than a magnitude 5?
- Two steps up.
- About $32 \times 32 \approx 1{,}000$ times the energy.
Answer: About 1,000 times
Common mistake
Reading magnitude like ordinary counting, so a magnitude 6 seems twice a magnitude 3. It is three steps bigger: waves $10^3 = 1{,}000$ times taller and about 32,000 times the energy. Check: subtract the magnitudes first, then multiply by 10 (or by about 32) once for each step.
Magnitude is different from intensity, which describes how strongly the ground shook at one place (the Modified Mercalli scale, I to XII). One earthquake has one magnitude but many intensities: strongest near the epicenter and weaker far away.