Earthquake Epicenter Finder
Three seismograph stations recorded the same earthquake. Read when the P and S waves arrived, turn each lag into a distance, and draw circles to triangulate where the quake began.
Guided example: an earthquake has just been recorded at three seismograph stations. Follow the four steps to find where it started. Hints tell you if a reading looks off.
- Read the seismograms
- Convert lag to distance
- Draw circles, click the epicenter
- Reveal and check
Ashford ASH
Not read yetClick where the first small wiggles start: the P wave.
Largest S-wave swing: 6.2 mm
Bayview BAY
Not read yetClick where the first small wiggles start: the P wave.
Largest S-wave swing: 2.4 mm
Cedar Ridge CDR
Not read yetClick where the first small wiggles start: the P wave.
Largest S-wave swing: 15.5 mm
Type a distance or drag a circle's edge. Then click where the three circles meet.
Place your guess on the map first.
Prefer a graph? Read distance off the travel-time graph
The S–P lag is the gap between the two lines. Slide along until the gap matches your lag, then read the distance below. Each station you measure gets a bar here.
How to find an earthquake’s epicenter
Seismologists locate earthquakes by comparing two kinds of waves. Both leave the focus at the same moment, but P waves are faster, so the gap between their arrivals grows with distance.
- Find the arrivals. On each seismogram, mark where the first small wiggles start (the P wave) and where the larger wiggles suddenly begin (the S wave).
- Measure the S–P lag. Subtract the P arrival time from the S arrival time.
- Convert the lag to distance. Multiply the lag in seconds by 8.4 to get kilometers, or read the distance off a travel-time graph.
- Draw a circle around each station. Its radius is that station’s distance. The quake happened somewhere on that circle.
- Find where the circles meet. Three circles cross at one point, the epicenter. If they leave a small triangle, the epicenter is in its middle.
Where does 8.4 come from?
After traveling d km, the S wave is behind the P wave by d ÷ 3.5 − d ÷ 6.0 seconds, about 0.119 s for every kilometer. Flip that around:
distance (km) = S–P lag (s) × 8.4
Worked example
This is the earthquake in Guided mode. Reading each arrival to the nearest 0.1 second gives these numbers:
| Station | P (s) | S (s) | S–P lag (s) | × 8.4 = distance |
|---|---|---|---|---|
| Ashford | 40.5 | 62.3 | 21.8 | 183 km |
| Bayview | 52.0 | 82.1 | 30.1 | 253 km |
| Cedar Ridge | 32.6 | 48.7 | 16.1 | 135 km |
Cedar Ridge has the shortest lag, so it is the closest station. Its seismogram, with both arrivals marked:
Drawing the three circles puts the epicenter 260 km east and 200 km south of the map’s north-west corner. Because the readings were rounded, the circles meet within about 0.5 km of that point rather than exactly on it.
Bonus, magnitude: Cedar Ridge’s largest S-wave swing was 15.5 mm. M ≈ log₁₀(15.5) + 3 × log₁₀(8 × 16.1) − 2.92 ≈ 4.6, a light quake that people nearby would feel. This formula is a classroom approximation of the Richter scale.
P waves vs S waves
P waves (primary)
- Push and pull the rock in the direction they travel, like a slinky.
- Fastest seismic waves: about 6.0 km/s in the upper crust in this lab.
- Travel through solids, liquids and gases.
- Arrive first, usually as small wiggles.
S waves (secondary)
- Shake the rock side to side, across the direction they travel.
- Slower: about 3.5 km/s in this lab.
- Travel only through solids, which is how we know Earth’s outer core is liquid.
- Arrive second, usually with much bigger swings.
Epicenter vs focus
The focus (or hypocenter) is the point underground where the rock first broke. The epicenter is the point on the surface directly above it. Most earthquakes start within a few tens of kilometers of the surface.
Triangulating with three stations, as in this lab, finds the epicenter. Working out the depth of the focus needs more stations and more careful timing.
Common mistakes
- Marking the biggest wiggle as the S wave. The S wave starts where the swings suddenly get bigger, before they reach their largest size.
- Using an arrival time instead of the lag. The distance comes from the gap between S and P, not from either time on its own.
- Dividing instead of multiplying. A longer lag means a farther station, so the distance must grow: lag × 8.4.
- Using the distance as a diameter. The distance is the circle’s radius, measured from the station outward.
- Expecting a perfect point. Small reading errors leave a small triangle; the epicenter is in its middle.
What this model simplifies
The finder keeps the physics the method depends on and leaves out the rest. Wave speeds are constant (6.0 and 3.5 km/s), waves travel in straight lines along a flat surface, and the focus is treated as if it were at the surface. In the real Earth, speeds change with rock type and depth, waves bend as they travel, and quakes start kilometers down, so seismologists use travel-time tables and many stations. The seismograms are synthetic: drawn from the model, not recorded. The magnitude formula, M ≈ log₁₀(A) + 3 × log₁₀(8 × Δt) − 2.92, is a classroom fit to the Richter scale, not an official magnitude.
Earthquake epicenter activity
A one-page printable worksheet for grades 6–10, about 15 minutes with Guided mode: a results table and six questions, from reading the lag to estimating the magnitude.
Share the lab with your class in one click. Students need no accounts or logins.
Share to Google ClassroomEpicenter questions
What is an earthquake’s epicenter?
The epicenter is the point on Earth’s surface directly above the focus, the place underground where the rock first slipped. News reports and maps give the epicenter because it is where the shaking is usually strongest at the surface.
Why do you need three seismograph stations?
One station tells you only how far away the earthquake was, so it could be anywhere on a circle around that station. Two circles usually cross at two points. A third circle passes through just one of those points, which is the epicenter. Real networks use many more stations to also work out the depth and the exact time the quake began.
How do you turn the S–P lag into a distance?
P waves travel faster than S waves, so the S wave falls further behind the farther it goes. In this lab P waves travel 6.0 km/s and S waves 3.5 km/s, so the S wave falls 1 second behind every 8.4 km. Multiply the lag in seconds by 8.4 to get the distance in kilometers, or read it off a travel-time graph.
Why don’t my three circles meet at exactly one point?
Small reading errors move each circle. A pick that is 1 second off changes a distance by 8.4 km, so the circles usually leave a small “error triangle”. The epicenter is in the middle of it. Real data adds more error, because rocks vary and waves travel deep below the surface.
How realistic is this simulation?
The method is the real one, and the wave speeds are typical of the upper crust, but the model is simplified: the speeds never change, the waves travel straight along the surface, and the focus is treated as if it were at the surface. Seismologists use travel-time tables built from real Earth structure instead. The magnitude formula is a classroom approximation, not an official magnitude.
Can I use the Epicenter Finder in class?
Yes. It is free with no sign-up and runs on school Chromebooks. Use Guided mode with the printable activity sheet, then let students try a three-quake Challenge. Teachers can find the answer key on the For teachers page.