P–S Wave Distance Calculator
Estimate source-path distance from a P/S arrival-time difference and entered wave speeds. Compare both travel times in a uniform-medium model.
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Result
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Calculation steps
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How to calculate
Both waves cover the same source-to-station path, with the P wave faster. Subtract their travel times, Δt=d/vS−d/vP, then solve for distance.
d=Δt vP vS/(vP−vS)
Worked example
WithvP=6000m/s, vS=3000m/s and an S−P lag of10s, path distance is60km. P travel time is10s and S travel time20s.
Assumptions and input details
Speeds must be positive withvP>vS; lag is nonnegative. Entered base quantities are capped at1e12. This is a straight common-path, constant-speed educational model. It estimates path distance, not a map location or surface epicentral distance without source depth. Real layered-Earth travel-time curves and refraction are outside this model.
References: OpenStax sound and seismic wave timing
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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