Epicenter Distance Calculator
When an earthquake happens, the first waves to reach a seismograph are the fast P waves. The slower S waves arrive later, and the gap between them grows with distance. Enter that gap, the S-P interval in seconds, and this calculator reads it off a travel-time curve to estimate how many kilometers away the epicenter is. The curve is a piecewise-linear lookup anchored on the IRIS and USGS teaching points, presented here for what it is: an approximation of the standard travel-time tables seismologists use, giving a fast estimate from a single station, not an official location.
This is not a general-purpose distance tool. A generic distance calculator measures between two points you already know. Here one of the points is unknown, and the only evidence is timing: the distance is inferred from how long the two wave types took to separate on a seismogram.
Quick Answer
An S-P interval of 8 seconds gives an estimated epicenter distance of 80.00 km: the interval is read off a travel-time curve anchored at 90 seconds to 900 km, 180 seconds to 1,800 km and 300 seconds to 3,300 km, with straight-line interpolation between the anchors. On that curve 60 seconds returns 600.00 km and 300 seconds (5 minutes) returns 3,300.00 km, as the comparison below shows.
Key takeaways
- One input only: the S-P interval in seconds. The tool does not accept the P and S arrival times separately and has no minutes mode, so convert minutes to seconds yourself.
- The distances come from a travel-time curve, not a single multiplier. The curve is anchored on the IRIS teaching points and approximates the standard travel-time tables, so it stays close at long range where the old flat × 8 classroom rule fell 20 to 27 percent low.
- One station gives a distance, never a location. The epicenter lies somewhere on a circle of that radius around the station; three or more stations fix the point.
- Zero is rejected by the tool. A zero interval would mean the waves arrived together, but the calculator asks for a positive number and shows an alert instead.
- Quick Answer
- How to use the epicenter distance calculator
- The travel-time curve, and where its points come from
- Worked example: an 8-second interval
- Why the curve replaced the flat rule: old rule versus this tool
- One station gives a circle, three give a location
- Epicenter, hypocenter and what this distance actually is
- What competing tools and methods miss
- Common mistakes with S-P distance estimates
- Frequently asked questions
How to use the epicenter distance calculator
You need one number from one seismogram, then one click. The results stay hidden until you click Calculate.
- Read the P arrival: the first sharp deflection on the seismogram is the P wave reaching the station. Note its time.
- Read the S arrival: the later, usually larger deflection is the S wave, on the same clock.
- Subtract: S time minus P time is the interval, in seconds. Arrivals at 12:00:00 and 12:00:08 give an interval of 8 seconds.
- Enter the interval and read the distance: the result is in kilometers, with the curve lookup shown so you can check it against the anchor points.
If your seismogram is scaled in minutes, this tool has no minutes setting: multiply by 60 before you type. Entering 5 for a five-minute interval returns 50.00 km, a small local tremor, not the event on your seismogram.
The travel-time curve, and where its points come from
Both wave types leave the earthquake at the same moment. The P wave travels faster, so the two arrival times separate by an amount that depends only on how far they traveled.
Curve anchors: 0 s → 0 km, 90 s → 900 km, 180 s → 1,800 km, 300 s → 3,300 km. Between anchors the tool interpolates in a straight line; beyond 300 s it continues at 12.5 km per second, the slope of the 180 to 300 s segment.
The anchors come from the S-P teaching points published by IRIS and republished by the Maryland Geological Survey: 1.5 minutes (90 seconds) to about 900 km, 3 minutes to about 1,800 km and 5 minutes to about 3,300 km. Reading distance off a curve through those points approximates the standard travel-time tables that the U.S. Geological Survey describes in its guide to seismographs and keeping track of earthquakes: the P-S interval at several stations is converted with standard travel-time tables and curves, not a single flat factor.
Historical note: the simple classroom rule this tool used before multiplied the interval by 8. That 8 was a rounding of (Vp × Vs) ÷ (Vp − Vs): with typical crustal speeds of about 6 km/s for P waves and about 3.5 km/s for S waves, the combination gives 8.4 km per second of interval. The old rule is kept here only as history, because it underestimates at range, about 20 percent low at 90 seconds and about 27 percent low at 300 seconds. One description to be careful with: some pages call that old 8 a "speed difference" between the waves. It is not. The difference between 6 km/s and 3.5 km/s is 2.5 km/s, and multiplying an interval by 2.5 would understate every distance roughly threefold.
Worked example: an 8-second interval
A station records a P arrival at 12:00:00 and an S arrival at 12:00:08.
| S-P interval | Distance this tool returns | Band shown with the result |
|---|---|---|
| 1 second | 10.00 km | Local |
| 8 seconds | 80.00 km | Local |
| 25 seconds | 250.00 km | Regional |
| 37.5 seconds | 375.00 km | Regional |
| 60 seconds | 600.00 km | Distant regional |
| 120 seconds | 1,200.00 km | Over 1,000 km |
Every row is a real run of this calculator, so you can type any of them in and get the same figures back.
Why the curve replaced the flat rule: old rule versus this tool
Wave speeds are not constant with depth. On longer paths the waves dive into deeper, faster rock, so each extra second of interval corresponds to more distance, and a flat multiplier falls further behind the standard curves as the interval grows. This tool therefore uses the curve itself. Educational material from the Incorporated Research Institutions for Seismology, republished by the Maryland Geological Survey, gives the travel-time reference points the curve is anchored on: a 1.5-minute interval corresponds to about 900 km, 3 minutes to about 1,800 km, and 5 minutes to about 3,300 km. Between those points the tool interpolates in a straight line, which keeps it an approximation of the full tables, not a replacement for them.
Read the pattern, not just the rows: at 90 seconds the old rule is about 20 percent low, and at 300 seconds about 27 percent low. This tool now follows the curve values at those points instead. For anything that feeds a decision, use the full travel-time tables and several stations, as seismic networks do.
One station gives a circle, three give a location
A single interval says how far, never which way: the epicenter could be anywhere on a circle around the station with the calculated distance as radius. A second station narrows it to the two points where two circles cross. A third station's circle passes through only one of them, and that point is the located epicenter, the method set out in the open textbook chapter on measuring and locating earthquakes.
Notice what kind of geometry that is: distances from known stations to an unknown point. It is not the coordinate geometry of a euclidean distance calculator, which measures between two points whose coordinates are both given, nor a three-point measurement like the distance between 3 points calculator, where all three points are known in advance. Here the third point is the answer, and the circles are how you find it.
Epicenter, hypocenter and what this distance actually is
The epicenter is the point on the surface directly above the hypocenter (or focus), where the rupture starts underground. The figure returned here is an epicentral distance: the surface distance from station to epicenter, read from a travel-time curve anchored on the IRIS teaching points.
Older versions of this page described the result as a straight-line distance. One qualification: for a shallow earthquake the straight line from station to hypocenter and the surface distance to the epicenter are nearly the same, but for a deep-focus earthquake, 100 km or more down, the true path is noticeably longer than the surface distance, and a single-station curve estimate cannot separate depth from distance at all. Deep events are where this tool is a rough scale indicator only.
What competing tools and methods miss
- Direct clones keep the flat rounding: BraveCalculator's epicenter distance tool still uses the flat × 8 rule and asks for the two arrival times separately, subtracting them for you. Convenient, but it describes the constant as a speed difference between the waves, which the factor is not, and it gives no warning about how far the rule drifts at long range. This tool uses the travel-time curve instead.
- Formula libraries mix intents: TrueGeometry's epicenter pages include a tool that averages two stations' coordinates and calls the midpoint an epicenter. An average of two station positions is not a location method at all: real location is the intersection of distance circles, as described above.
- Downstream tools need this number first: Calculator City's earthquake magnitude calculator takes amplitude and distance to the epicenter as inputs, and CalculatorUltra's attenuation tool takes magnitude and distance to estimate ground motion. Both assume a distance you may not have yet. This tool produces that first number, with its limits stated. Full location exercises such as the Virtual Earthquake lab teach the complete three-station method, but they are lessons, not ten-second estimates.
Common mistakes with S-P distance estimates
- Entering minutes as seconds. The largest error available here shrinks the answer sixty-sixfold: a 5-minute interval entered as 5 returns 50.00 km instead of 3,300.00 km.
- Entering an arrival time instead of the interval. The tool wants the difference between the two arrivals. A clock time, or the P travel time alone, produces a meaningless number.
- Reading the surface waves as the S arrival. On a distant seismogram the large surface wave train arrives after the S wave. Picking it inflates the interval and the distance.
- Expecting a location from one station. A distance plus no direction is a circle. Reporting a town name from a single interval is a guess dressed as a measurement.
- Using the estimate for response decisions. Emergency decisions run on agency locations built from many stations and travel-time tables. A single-station result is a learning and orientation aid.
Frequently asked questions
Read the S-P interval, the S arrival time minus the P arrival time in seconds, off a travel-time curve anchored at 90 seconds to 900 km, 180 seconds to 1,800 km and 300 seconds to 3,300 km, interpolating in a straight line between the anchors. An interval of 8 seconds gives 80.00 km, and an interval of 60 seconds gives 600.00 km. The P wave arrives first because it travels faster, and the gap between the two arrivals grows with the distance traveled, which is what makes the interval a distance measurement.
From teaching material published by IRIS, the Incorporated Research Institutions for Seismology, and republished by the Maryland Geological Survey: a 90-second interval corresponds to about 900 km, a 180-second interval to about 1,800 km and a 300-second interval to about 3,300 km. This tool anchors its curve on those points and interpolates between them, approximating the standard travel-time tables seismologists use. The older classroom shortcut multiplied the interval by 8, a rounding of the 8.4 km per second figure from typical crustal speeds of about 6 km/s for P waves and 3.5 km/s for S waves, but that flat rule runs well low at long range, which is why this tool no longer uses it.
It is a curve-based estimate that follows the IRIS teaching points exactly at the anchors: 90 seconds gives 900 km, where the old flat rule gave 720 km, about 20 percent low, and 300 seconds gives 3,300 km, where the old rule gave 2,400 km, about 27 percent low. Between the anchors it interpolates in a straight line, so it remains an approximation of the full travel-time tables, because waves on longer paths travel through deeper, faster rock. Professional locations use those full tables and many stations instead.
No. One station gives only a distance, so the epicenter lies somewhere on a circle of that radius around the station, in any direction. Two stations narrow it to the two points where their circles cross, and a third station's circle passes through only one of them. Locating an epicenter therefore takes at least three stations, which is why this calculator is named for distance, not location.
No. This tool has a single input: the difference between the two arrival times, in seconds. Subtract the P arrival from the S arrival yourself and enter the result. For arrivals at 12:00:00 and 12:00:08, the value to enter is 8, and the calculator returns 80.00 km.
Multiply the minutes by 60 and enter the seconds, because the tool has no minutes mode. A 5-minute interval is 300 seconds, which returns 3,300.00 km on the travel-time curve. Entering 5 instead returns 50.00 km, a sixty-sixfold understatement. At intervals of several minutes the curve matters most, as the comparison on this page shows.
The calculator rejects it and asks for a valid positive number. A zero interval would mean both waves arrived at the same instant, which happens only when the station is effectively at the epicenter, but this tool does not return 0 km: zero, negative and empty entries are treated as invalid. The smallest usable inputs are small positive intervals such as 0.5 seconds, which returns 5.00 km.
It is an estimate of the epicentral distance: the surface distance from the station to the epicenter, the point on the surface above the underground hypocenter where the rupture started. For shallow earthquakes the two distances are nearly equal. For deep-focus earthquakes the true path from the hypocenter to the station is longer than the surface distance, and a single-station curve estimate cannot separate the depth from the distance.
Add This Calculator to Your Website
Embed this calculator on your own site with the code below. Pick a size to preview it live, then copy the code.
Powered by Calculator Zilo
References
- U.S. Geological Survey. Seismographs: keeping track of earthquakes, including the P-S interval method and travel-time tables. Accessed October 21, 2026.
- Incorporated Research Institutions for Seismology (IRIS), via Maryland Geological Survey. Locating earthquakes from S-P times: educational material with interval-to-distance examples. Accessed October 21, 2026.
- Dynamic Planet (open textbook), Maricopa Community Colleges. Measuring and locating earthquakes: triangulation from three or more stations. Accessed October 21, 2026.
- Braile, L., Purdue University. Earthquake location exercise: measuring S minus P times and reading epicenter distance from travel-time curves (PDF). Accessed October 21, 2026.
- BraveCalculator. Epicenter distance calculator: a flat S-P times 8 rule with separate arrival-time fields. Accessed October 21, 2026.