Home·Earthquake magnitude

111 magnitudes — a 7 is not twice a 6 but thirty-two times

Magnitude is a logarithmic scale, so one step is a multiplication. The base-ten log of the energy is 1.5 × magnitude + 4.8, which makes one whole point worth 31.6 times the energy and two points exactly a thousand. Here are 111 steps of 0.05 from 4.0 to 9.5.

Hiroshima bombs

  • M 5.00.032
  • M 6.01
  • M 7.032
  • M 8.01,005
  • M 9.031,792

One step is a multiplication

The base-ten log of the energy is 1.5 × magnitude + 4.8. With a slope of 1.5, one point of magnitude means ten to the power 1.5, or 31.6 times the energy. Two points make ten cubed — a thousand times exactly. In other words, thirty-odd magnitude-6 quakes fit inside a single 7.

Shaking ×10, energy ×31.6

One point of magnitude multiplies the amplitude a seismograph traces by ten, but the released energy by 31.6. The two differ because energy depends not only on how far the ground moves but on how long it shakes and how much fault surface tore. When the news says “ten times” it means the shaking; “thirty-two times” means the energy.

Yardsticks to compare against

Written in joules the numbers run to ten to the twentieth and stop meaning anything, so tonnes of TNT and Hiroshima bombs are given alongside. Magnitude 6.0 is about one such bomb; magnitude 9.0 is more than thirty thousand of them. This compares released energy only — not damage.

Magnitude is not intensity

Magnitude describes the energy the earthquake itself released, so there is one number per quake. Intensity describes how hard a particular place shook, so it differs from street to street. A shallow magnitude-5 directly underfoot can shake harder than a deep magnitude-7 far away — depth, distance and ground conditions decide intensity.

Magnitudes get revised

The first number announced for a large earthquake is often revised by a tenth or three later on, as more records arrive and the ruptured fault is re-measured. That is why the steps here are 0.05: rounding to a single decimal would hide exactly those revisions.

Find it by magnitude

In TNT

M 5.0 – 5.95

M 5.00
10^2.68 t
M 5.05
10^2.75 t
M 5.10
10^2.83 t
M 5.15
10^2.9 t
M 5.20
10^2.98 t
M 5.25
10^3.05 t
M 5.30
10^3.13 t
M 5.35
10^3.2 t
M 5.40
10^3.28 t
M 5.45
10^3.35 t
M 5.50
10^3.43 t
M 5.55
10^3.5 t
M 5.60
10^3.58 t
M 5.65
10^3.65 t
M 5.70
10^3.73 t
M 5.75
10^3.8 t
M 5.80
10^3.88 t
M 5.85
10^3.95 t
M 5.90
10^4.03 t
M 5.95
10^4.1 t

M 6.0 – 6.95

M 6.00
10^4.18 t
M 6.05
10^4.25 t
M 6.10
10^4.33 t
M 6.15
10^4.4 t
M 6.20
10^4.48 t
M 6.25
10^4.55 t
M 6.30
10^4.63 t
M 6.35
10^4.7 t
M 6.40
10^4.78 t
M 6.45
10^4.85 t
M 6.50
10^4.93 t
M 6.55
10^5 t
M 6.60
10^5.08 t
M 6.65
10^5.15 t
M 6.70
10^5.23 t
M 6.75
10^5.3 t
M 6.80
10^5.38 t
M 6.85
10^5.45 t
M 6.90
10^5.53 t
M 6.95
10^5.6 t

M 7.0 – 7.95

M 7.00
10^5.68 t
M 7.05
10^5.75 t
M 7.10
10^5.83 t
M 7.15
10^5.9 t
M 7.20
10^5.98 t
M 7.25
10^6.05 t
M 7.30
10^6.13 t
M 7.35
10^6.2 t
M 7.40
10^6.28 t
M 7.45
10^6.35 t
M 7.50
10^6.43 t
M 7.55
10^6.5 t
M 7.60
10^6.58 t
M 7.65
10^6.65 t
M 7.70
10^6.73 t
M 7.75
10^6.8 t
M 7.80
10^6.88 t
M 7.85
10^6.95 t
M 7.90
10^7.03 t
M 7.95
10^7.1 t

M 8.0 – 8.95

M 8.00
10^7.18 t
M 8.05
10^7.25 t
M 8.10
10^7.33 t
M 8.15
10^7.4 t
M 8.20
10^7.48 t
M 8.25
10^7.55 t
M 8.30
10^7.63 t
M 8.35
10^7.7 t
M 8.40
10^7.78 t
M 8.45
10^7.85 t
M 8.50
10^7.93 t
M 8.55
10^8 t
M 8.60
10^8.08 t
M 8.65
10^8.15 t
M 8.70
10^8.23 t
M 8.75
10^8.3 t
M 8.80
10^8.38 t
M 8.85
10^8.45 t
M 8.90
10^8.53 t
M 8.95
10^8.6 t

M 9.0 – 9.95

M 9.00
10^8.68 t
M 9.05
10^8.75 t
M 9.10
10^8.83 t
M 9.15
10^8.9 t
M 9.20
10^8.98 t
M 9.25
10^9.05 t
M 9.30
10^9.13 t
M 9.35
10^9.2 t
M 9.40
10^9.28 t
M 9.45
10^9.35 t
M 9.50
10^9.43 t

M 4.00 – 4.95

M 4.00
10^1.18 t
M 4.05
10^1.25 t
M 4.10
10^1.33 t
M 4.15
10^1.4 t
M 4.20
10^1.48 t
M 4.25
10^1.55 t
M 4.30
10^1.63 t
M 4.35
10^1.7 t
M 4.40
10^1.78 t
M 4.45
10^1.85 t
M 4.50
10^1.93 t
M 4.55
10^2 t
M 4.60
10^2.08 t
M 4.65
10^2.15 t
M 4.70
10^2.23 t
M 4.75
10^2.3 t
M 4.80
10^2.38 t
M 4.85
10^2.45 t
M 4.90
10^2.53 t
M 4.95
10^2.6 t

How to read this

  • log10(energy) = 1.5 × magnitude + 4.8, with energy in joules.
  • One point of magnitude is 31.6 times the energy; two points exactly a thousand.
  • The amplitude grows tenfold, the energy 31.6-fold.
  • Magnitude belongs to the quake; intensity differs from place to place.

Frequently asked questions

Q. How much bigger is a 7 than a 6?

31.6 times in energy — ten times in the amplitude a seismograph records.

Q. And two points apart?

Exactly a thousand times, because that is ten cubed.

Q. Why is the shaking ten but the energy 31.6?

Energy depends not only on how far the ground moves but on how long it shakes and how much fault surface tore.

Q. What is the difference between magnitude and intensity?

Magnitude belongs to the earthquake — one number. Intensity is how hard one place shook, and it differs from place to place.

Q. Why steps of 0.05?

Large quakes are often revised by a tenth or three after the first announcement. Rounding to one decimal would hide exactly those revisions.