How Are Earthquakes Measured? Why M8 Isn't Twice M4

Earthquakes are measured with seismometers, instruments that record the ground shaking as a wiggly line called a seismogram. From those recordings, scientists work out the magnitude: one number for the size of the earthquake at its source, on the moment magnitude scale. Each step up means about 32 times more energy, so M8 isn't twice M4.

In this post, we'll see why the scale is logarithmic. Each whole step makes the waves on the seismogram 10 times taller, so a magnitude 8, four steps above a magnitude 4, releases 32 × 32 × 32 × 32, about a million times the energy. Then we'll find an epicentre with three seismometers and meet intensity: how hard the ground shakes where you are. Last, we'll see why nobody uses the Richter scale for big earthquakes any more, and work out the gap between the first jolt and the strong shaking, the head start that earthquake early warning is built on.

This post goes with letsBug Geography, episode 2. It carries on from episode 1, where plates lock together and then suddenly slip, and episode 3 moves on to reading a climate graph. Watch the lesson, or read on: the post adds a full magnitude table, the maths behind 32, worked examples and practice questions with answers.

How many times stronger is each magnitude step?

Here's the short answer in one table. Count the whole steps between the two magnitudes, then read across.

The wave height goes up 10 times per step. The energy goes up 10^1.5 = 31.6 times per step, so 2 steps is 10³ = 1,000 times and 4 steps is 10⁶ = 1,000,000 times. The sections below show where those numbers come from.

How are earthquakes measured? Seismometers and seismic waves

An earthquake starts underground, where the rock suddenly breaks and slips along a fault. That point is the focus. The point on the surface directly above it is the epicentre. From the focus, energy spreads out through the rock as seismic waves: vibrations that travel through the Earth and get recorded by instruments called seismographs (USGS).

A seismometer (also called a seismograph) works on a neat trick called inertia: a hanging mass tends to stay still when the ground moves (BGS). The ground, and the case around the mass, move; the mass stays put, and the difference is recorded as a seismogram. Two kinds of wave travel through the rock to it, and a third kind travels along the surface:

• P waves (primary) squeeze and stretch the rock along the direction they travel. P stands for primary, because they're the fastest waves (British Geological Survey): about 5 to 7 km/s in typical crust.
• S waves (secondary, or shear) shake the rock from side to side, across the direction they travel. S stands for shear or secondary, because they're slower than P waves: about 3 to 4 km/s in the crust.
• Surface waves form where P and S waves reach the Earth's surface, and roll along the ground. The BGS says they arrive last, after the P and S waves, and they often shake the ground much more than the P and S waves do.

Hold on to that gap between P and S. It's what earthquake early warning is built on, later in this post.

What is earthquake magnitude? One number for the size at the source

The USGS sums it up in two sentences: "Magnitude is the size of the earthquake. An earthquake has a single magnitude." Seismologists work it out from the seismograms recorded at many stations. Even Richter's original method adjusted for how far each seismograph was from the epicentre.

Today the standard is the moment magnitude scale, written Mw. Instead of only measuring how tall the wiggles are, it's based on the physics of the break: the strength of the rock, the area of the fault that slipped, and how far it moved (USGS). A bigger fault area or a longer slip gives a bigger magnitude.

The scale is logarithmic, which means each whole step multiplies instead of adding:

• Wave height: each whole number up is "a tenfold increase in measured amplitude as measured on a seismogram" (USGS). Amplitude is the height of the wiggle.
• Energy: each whole number up "represents an 32 times more energy release" (USGS, typo theirs).

Where does 32 come from? The energy goes up by 10 to the power 1.5 for every whole step. 10^1.5 = 31.6, which rounds to 32. That's why the USGS booklet The Severity of an Earthquake says "about 31 times" and its newer pages say 32: the same number, rounded differently. Wikipedia's moment magnitude article gives the general rule: the energy ratio between two earthquakes is 10^{1.5 × (difference in magnitude)}.

Is a magnitude 8 twice as strong as a magnitude 4?

Going from 4 to 8 is four steps. Each step multiplies, so let's build it up:

So a magnitude 8 makes waves 10,000 times taller on the seismogram and releases about a million times the energy of a magnitude 4. With the rounded 32 you get 32 × 32 × 32 × 32 = 1,048,576; with the exact 10^1.5 it's 10⁶ = 1,000,000 exactly. Either way: about a million, not 2.

Decimals count too. A magnitude 6.5 against a 6.0 is half a step: 10^0.75 = about 5.6 times the energy. That's why a news report that upgrades an earthquake "from 6.0 to 6.5" is a big change, not a small one.

Is it still the Richter scale?

Not for big earthquakes. Charles Richter invented the idea of magnitude in 1935, for earthquakes in southern California. The USGS notes that his first version only worked for California earthquakes within 600 km of one particular type of seismograph. It worked well for small, nearby earthquakes, but it can't keep up with very large ones. The British Geological Survey says "Richter’s original magnitude scale underestimates the size of large events", a problem called saturation: for very big earthquakes, the number comes out too low.

That's why moment magnitude replaced it. The USGS says the Richter scale "is not commonly used anymore, except for small earthquakes recorded locally", and that for very large earthquakes, moment magnitude gives the most reliable size. Moment magnitude was designed to give roughly the same numbers as the Richter scale where the two overlap, so old and new values still line up for small earthquakes.

What is the difference between magnitude and intensity?

Magnitude is one number for the whole earthquake. Intensity is how strongly the ground shook at one particular place, judged by what people felt and what got damaged. It changes from place to place, mostly with distance from the part of the fault that broke (USGS).

The scale used in the United States is the Modified Mercalli Intensity scale, developed in 1931 by Harry Wood and Frank Neumann. It has 12 levels written in Roman numerals, from I to XII. The low numbers describe what people feel; the high numbers describe damage to buildings:

• I: "Not felt except by a very few under especially favorable conditions."
• VI: "Felt by all, many frightened."
• XII: "Damage total. Lines of sight and level are distorted. Objects thrown into the air."

Unlike magnitude, the USGS says it "does not have a mathematical basis; instead it is an arbitrary ranking based on observed effects." There's no ×32 rule here.

Intensity depends on more than distance. Depth and the ground under you matter too. The USGS compares two earthquakes in the United States: the M6.7 Northridge, California, earthquake shook harder, and over a wider area, than the slightly larger M6.8 Nisqually, Washington, earthquake. Northridge started about 5 to 18 km down (3 to 11 miles); Nisqually about 48 to 58 km down (30 to 36 miles). A smaller magnitude, closer to the surface, shook harder.

Bigger isn't always deadlier: Chile 2010 vs Nepal 2015

On 27 February 2010, a magnitude 8.8 earthquake struck Maule, Chile. On 25 April 2015, a magnitude 7.8 earthquake struck Nepal (both are the USGS's moment magnitudes). Chile's was one whole step bigger, so it released about 32 times the energy.

Yet about 525 people died in Chile, and 8,962 in Nepal: about 17 times as many. (Those are Wikipedia's totals. The USGS's own summaries say "At least 523 people killed" in Chile and "At least 8,669 people killed" in Nepal, counting a magnitude 7.3 aftershock on 12 May. Either way, about 17 times as many.) Why?

• Buildings. Chile's newer seismic building codes took effect in 1985. A Seattle City Council report on the lessons from Chile found that "Of the 9,974 modern mid and high rises that had been constructed since 1985, when the new seismic codes took effect, only 35 had to be evacuated". That's 0.35%. Most of the deaths in buildings were in "old-style adobe houses".
• The tsunami. In Chile, many of the deaths were from the tsunami that followed, not from collapsing buildings. A field survey of the tsunami found that "Many of the tsunami victims were tourists in coastal campgrounds", while most people living on the coast evacuated on their own after the shaking (Fritz and others, 2011).
• Vulnerability in Nepal. Experts had warned for decades that Nepal was vulnerable, "particularly because of its geology, urbanization, and architecture" (Wikipedia, April 2015 Nepal earthquake).

Intensity tells the same story: Wikipedia gives Chile's strongest shaking as Mercalli IX and Nepal's as X, even though Nepal's magnitude was lower. Nepal's earthquake started about 8 km down, Chile's about 23 km down (USGS).

India has its own example. On 26 January 2001, Republic Day, at 8:46 in the morning India time (03:16 UTC), a magnitude 7.7 earthquake struck near Bhachau in Kutch, Gujarat, about 16 km down. It's known as the Bhuj earthquake. The USGS summary counts "At least 20,005 people killed, 166,836 injured" in Bhuj, Ahmedabad, Rajkot and other parts of Gujarat, and says it was "Felt throughout northern India and much of Pakistan." Its cause is the one from episode 1: the Indian plate pushing north into the Eurasian plate (USGS). Chile 2010 was 1.1 steps bigger, so it released about 45 times the energy of Bhuj (10^{1.5 × 1.1} = 44.7). Yet, using the USGS's own counts, Bhuj killed about 38 times as many people.

Bhuj also shows that agencies can give slightly different numbers for the same earthquake. The USGS gives magnitude 7.7; the International Seismological Centre gives 7.6 (Wikipedia). It's still one earthquake with one size: the two estimates just differ a little.

How do earthquake early warnings reach your phone?

Your phone buzzes "Earthquake!" a few seconds before the shaking. That isn't a prediction. The earthquake has already started, and the alert is winning a race against the S waves.

On the west coast of the United States, the USGS-run ShakeAlert system "detects significant earthquakes quickly enough so that alerts can be delivered to people and automated systems potentially seconds before strong shaking arrives." It serves over 50 million residents and visitors in California, Oregon and Washington. Its fastest method uses the P waves: as soon as seismometers at "at least four stations" near the earthquake pick them up, it estimates the earthquake's magnitude, epicentre and start time. Wikipedia's early warning article sums up the idea: "When P waves are detected, the readings are analysed immediately", and the warning goes out to phones, radio, television and sirens before the S waves arrive. The alert travels over networks, not through rock, so a town far from the epicentre can get it before the shaking reaches it. Those seconds are enough to "Drop, Cover, and Hold On", and ShakeAlert lists automatic actions such as "slowing trains, closing water valves, turning on backup generators".

Worked example. A town is 120 km from the epicentre. P waves travel at about 6 km/s and S waves at about 4 km/s. How long is the gap between the first jolt and the strong shaking?

1. Units first: time = distance ÷ speed, and km ÷ km/s = s.
2. P waves: 120 ÷ 6 = 20 s.
3. S waves: 120 ÷ 4 = 30 s.
4. Gap: 30 − 20 = 10 s between the first jolt and the strong shaking. A seismometer in the town gets that much warning; a network like ShakeAlert, which spots the quake near the epicentre and sends the alert at network speed, can sometimes give more, minus a few seconds to process.

Close to the epicentre, the P and S waves arrive almost together, so the gap shrinks to almost nothing, and there's almost no time for any alert. Further away, the gap grows.

How do scientists find the epicentre? Triangulation with three seismometers

The P-to-S gap has a second job: it tells a seismometer how far away the earthquake was. The USGS compares it to lightning and thunder. You see the flash first and hear the thunder later, and the further away the storm, the longer the wait. P waves are the flash; S waves are the thunder.

Let's turn the gap into a distance. With our example speeds (P at 6 km/s, S at 4 km/s), the gap is the S time minus the P time: d ÷ 4 − d ÷ 6 = d ÷ 12, where d is the distance in km. So every second of gap means 12 km. Check it against the worked example above: 120 km gave a 10 s gap, and 10 × 12 = 120.

One distance isn't enough, though. A single seismometer can't tell which direction the earthquake came from, only how far away it was (USGS). So the epicentre could be anywhere on a circle around that station. A second station gives a second circle, and two circles usually cross at two points. A third circle picks one of them. The BGS puts the method in one line: "The earthquake occurred at the point where all three circles intersect." That's triangulation: three stations, three circles, one point.

Worked example. Three stations record the same earthquake. Station A sees a 5 s gap, station B a 10 s gap and station C a 15 s gap. Where was the epicentre?

1. Distances: A: 5 × 12 = 60 km. B: 10 × 12 = 120 km. C: 15 × 12 = 180 km.
2. Circles: on a map, draw a circle around each station with that radius: 60 km around A, 120 km around B and 180 km around C.
3. Crossing point: all three circles meet at just one point, the epicentre. On the map below, it's 36 km east and 48 km south of station A. Check with Pythagoras: 36² + 48² = 1,296 + 2,304 = 3,600, and √3,600 = 60 km, the distance from A.

Real networks do the same sum with many more stations, worked out by computer. ShakeAlert's fastest method needs P waves at four or more stations before it estimates the epicentre.

Can earthquakes be predicted?

No. The USGS answers its own question in one word, then: "Neither the USGS nor any other scientists have ever predicted a major earthquake." A real prediction would have to give three things: the date and time, the location and the magnitude. Nobody can do that.

What scientists can do is forecast: the USGS can only work out the chance of a strong earthquake in an area within a certain number of years, shown on its hazard maps. A forecast says how likely; a prediction would say exactly when. And early warning is neither: it only starts once the earthquake has begun.

Don't mix it up with the volcano scale

Volcanic eruptions have their own scale, the Volcanic Explosivity Index (VEI), from 0 to 8. It's based mainly on how much material an eruption throws out and how high it goes. From VEI 2 upwards each step is 10 times as much, not 32:

Practice questions

Q1. A news alert says a magnitude 5.0 earthquake hit one region, and a week later a magnitude 7.0 hit another. How many times more energy did the second one release?

Q2. A town is 60 km from an epicentre. P waves travel at 6 km/s and S waves at 4 km/s. How long is the gap between the P waves and the S waves arriving there?

Q3. After an earthquake, a friend in a city near the epicentre says "it was a magnitude 7 here", and a friend 300 km away says "it was only a magnitude 4 here". What have they mixed up?

Q4. A report upgrades an earthquake from magnitude 6.0 to 6.5. Is that a small change?

Q5. A seismometer records a 20-second gap between the P waves and the S waves. Using P at 6 km/s and S at 4 km/s, how far away was the earthquake? Can this one station tell you where the epicentre was?

Keep going

• Watch the full lesson, How Are Earthquakes Measured? Why M8 Isn't Twice M4.
• Why earthquakes happen in the first place, plates that lock and slip: why do earthquakes and volcanoes happen? (Geography, episode 1).
• Next in letsBug Geography: how to read a climate graph, with Mumbai's monsoon and London on the same scales.
• How an alert reaches millions of phones in seconds: how the internet works.
• Another system that measures the Earth from signals and time: how GPS works without internet.

Checked on 20 October 2026 against the 25 sources below.

Sources

• USGS: The Severity of an Earthquake (seismographs, tenfold amplitude, about 31 times the energy, the 12 Mercalli levels), Earthquake Magnitude, Energy Release, and Shaking Intensity (single magnitude, 32 times the energy, Richter 1935 and 600 km, moment magnitude, Northridge and Nisqually, magnitude 10), The Modified Mercalli Intensity Scale, Moment magnitude, Richter scale: the different magnitude scales and Can you predict earthquakes?
• USGS: The Science of Earthquakes (lightning and thunder, triangulation with three seismographs), Earthquake Sequence Product (people begin to feel earthquakes at about M2.5) and the Hawaiian Volcano Observatory's "Felt" earthquakes (felt reports above about M3.0; depth and soil matter)
• USGS earthquake catalogue: M 8.8, 2010 Maule, Chile and M 7.8, Nepal 2015 (magnitude, date, depth, deaths) and M 9.5, 1960 Great Chilean Earthquake (the largest in the catalogue; date, deaths, tsunami) and M 7.7, 2001 Gujarat (Bhuj) (magnitude, date, depth, deaths, cause)
• British Geological Survey: How are earthquakes detected? (seismometers, P, S and surface waves and their speeds, locating an epicentre with three stations, Richter and moment magnitude, intensity) and How can earthquake magnitudes be negative? (below magnitude 2, not usually felt)
• IRIS (EarthScope): How are earthquakes located? (the gap grows with distance; three circles meet at the epicentre)
• ShakeAlert: home page (earthquake early warning on the US west coast) and ShakeAlert system algorithms (P-wave detection)
• Wikipedia: Earthquake warning system (how alerts beat the S waves)
• Seattle City Council: Earthquake lessons from Chile (building codes since 1985, 35 of 9,974 buildings, adobe houses)
• Fritz and others (2011), Field Survey of the 27 February 2010 Chile Tsunami, Pure and Applied Geophysics (tsunami victims, evacuation)
• Wikipedia: Moment magnitude scale (10^1.5 per step, saturation), 2010 Chile earthquake (525 dead, intensity IX), April 2015 Nepal earthquake (8,962 dead, intensity X), Volcanic explosivity index and 2001 Gujarat earthquake (Republic Day, Kutch, the International Seismological Centre's 7.6)

Every number in this post was checked against these sources, and the arithmetic was run in Python before publishing.