Earthquake magnitudes are logarithmic. One whole step on the scale means about 10 times more ground-motion amplitude on a seismogram and about 32 times more energy, so a magnitude 7 releases roughly 1,000 times the energy of a magnitude 5. That is hard to picture, which is why the energy is often compared with explosions: a magnitude 5.8 quake releases about as much energy as 7,500 tonnes of TNT, half a Hiroshima bomb.
Seismologists today report the moment magnitude (Mw), which is based on the seismic moment – the rigidity of the rock times the area of the fault that slipped times the average slip. It replaced Richter’s original local magnitude, which saturates for large quakes, but both agree reasonably well for moderate events. The energy relation log E = 1.5 M + 4.8 comes from Gutenberg and Richter.
Magnitude is a single number for the whole earthquake; intensity describes the shaking at a place. The calculator gives the typical maximum Modified Mercalli intensity near the epicentre for each magnitude, as in the USGS comparison table, plus the class name and how many such earthquakes happen worldwide each year.
How to use the Earthquake Calculator
- What do you want to do?
- Moment magnitude (Mw)
- Energy released
- Event
- Number of events
- First magnitude
- Second magnitude
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose what you know – a magnitude, an energy, a number of reference events or two magnitudes to compare. The calculator converts everything to an equivalent moment magnitude, then to energy and seismic moment, and divides by the energy of each reference event.
Worked example
For magnitude 5.8: log₁₀ E = 1.5 × 5.8 + 4.8 = 13.5, so E = 1013.5 ≈ 3.16 × 10¹³ J. Dividing by 4.184 × 10⁹ J per tonne gives about 7,558 t of TNT, or 0.50 Hiroshima bombs. Comparing it with a magnitude 7.1 quake: the amplitude ratio is 101.3 ≈ 20 and the energy ratio is 101.95 ≈ 89.
Magnitude, energy and effects
| Magnitude | Energy | TNT equivalent | Per year worldwide |
|---|---|---|---|
| 4 | 6.3 × 10¹⁰ J | 15 t | ≈ 13,000 |
| 5 | 2.0 × 10¹² J | 480 t | ≈ 1,300 |
| 6 | 6.3 × 10¹³ J | 15 kt | ≈ 130 |
| 7 | 2.0 × 10¹⁵ J | 480 kt | ≈ 15 |
| 8 | 6.3 × 10¹⁶ J | 15 Mt | ≈ 1 |
| 9 | 2.0 × 10¹⁸ J | 480 Mt | Rare |
Tips
- Use decimal degrees (negative for south and west) or the degrees–minutes–seconds fields.
- Great-circle distances assume a spherical Earth (error under 0.5%).
- Every field has its own unit menu.
- Everything is calculated in your browser.
Common mistakes to avoid
- Swapping latitude and longitude.
- Forgetting the minus sign for southern and western coordinates.
- Mixing magnetic and true north for bearings.
Inputs explained
| Field | What to enter |
|---|---|
| What do you want to do? | Choose one: Magnitude → energy, Energy → magnitude, Equivalent event → magnitude, Compare two magnitudes |
| Moment magnitude (Mw) | A number |
| Energy released | Units: t TNT, kt TNT, Mt TNT, J, GJ, TJ … |
| Event | Choose one: 1 tonne of TNT, Hiroshima bomb (≈ 15 kt), Nagasaki bomb (≈ 21 kt), Tsar Bomba, largest nuclear test (≈ 50 Mt) … |
| Number of events | A number |
| First magnitude | A number |
| Second magnitude | A number |
What each result means
- Energy released = 10^(1.5×[Moment magnitude] + 4.8)
- Energy released = [Energy released]
- TNT equivalent = [Energy released]÷4.184e9
- Hiroshima bombs = [Energy released]÷6.276e13
- Nagasaki bombs = [Energy released]÷8.786e13
- Tsar Bombas = [Energy released]÷2.092e17
- Krakatoa eruptions = [Energy released]÷8.368e17
- Share of the 1960 Chile earthquake = [Energy released]÷1.1220e19
- Seismic moment = 10^(1.5×[Moment magnitude] + 9.1)
- Amplitude ratio (second ÷ first) = 10^([Second magnitude] – [First magnitude])
- Energy ratio (second ÷ first) = 10^(1.5×([Second magnitude] – [First magnitude]))
- Energy of the first earthquake = 10^(1.5×[First magnitude] + 4.8)
- Energy of the second earthquake = 10^(1.5×[Second magnitude] + 4.8)
Formula
log₁₀ E = 1.5 M + 4.8 (E in joules) · M₀ = 10^(1.5 M + 9.1) N·m · Amplitude ratio = 10^(M₂ − M₁) · Energy ratio = 10^(1.5 (M₂ − M₁)) · 1 t TNT = 4.184 × 10⁹ J
Worked example
Inputs — What do you want to do?: Magnitude → energy; Moment magnitude (Mw): 5.8.
Results — Energy released = 31,622,776,601,683.793 J; TNT equivalent = 7,558 t TNT; Hiroshima bombs = 0.5039; Nagasaki bombs = 0.3599; Tsar Bombas = 0.000151; Krakatoa eruptions = 0.0000378; Share of the 1960 Chile earthquake = 0.00000282; Seismic moment = 6.3096e17 N·m; Magnitude class = Moderate; Typical maximum Mercalli intensity = VI–VII – felt by all, slight to moderate damage; Similar earthquakes worldwide per year (USGS estimate) = About 1,300.
Key terms
- Moment magnitude (Mw)
- Magnitude derived from the seismic moment; the standard scale for medium and large earthquakes.
- Seismic moment (M₀)
- Rock rigidity × fault area × average slip, in newton-metres.
- Modified Mercalli intensity
- A I–XII scale of the effects of shaking at a location.
- TNT equivalent
- Energy expressed as the mass of TNT releasing the same energy (4.184 GJ per tonne).
Frequently asked questions
How much stronger is a magnitude 7 than a magnitude 5?
About 100 times the ground-motion amplitude and about 1,000 times (10³) the energy.
How much energy does a magnitude 5.8 earthquake release?
About 3.2 × 10¹³ J – the energy of about 7,558 tonnes of TNT or half a Hiroshima bomb.
What magnitude is equal to the Nagasaki bomb?
One 21-kiloton bomb releases about 8.8 × 10¹³ J, the energy of a magnitude 6.1 earthquake.
What is the difference between magnitude and intensity?
Magnitude measures the size of the earthquake at its source; intensity (Modified Mercalli, I–XII) describes how strongly it is felt and the damage at a particular place.
Is the Richter scale still used?
Seismologists now report moment magnitude (Mw), which works for the largest earthquakes; news reports often still say "Richter scale".
What was the largest earthquake ever recorded?
The 1960 Valdivia, Chile, earthquake of magnitude 9.5, releasing about 1.1 × 10¹⁹ J.
How many earthquakes happen each year?
USGS estimates about 15 of magnitude 7–7.9, about 130 of magnitude 6–6.9 and about 1,300 of magnitude 5–5.9 worldwide.