Mathematics · Statistics

Seismic P-to-S Wave Velocity Ratio Calculator

Calculate p-to-s velocity ratio from compressional p-wave speed and shear s-wave speed.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
P-to-S velocity ratio1.746479

Calculation steps

  1. Use c=a/b with compressional P-wave speed=6.2 and shear S-wave speed=3.55.
  2. P-to-S velocity ratio=1.7464788732394367.

Understand Seismic P-to-S Wave Velocity Ratio

One idea, three depths

Choose how deeply to explain Seismic P-to-S Wave Velocity Ratio

Seismic P-to-S Wave Velocity Ratio: Calculate p-to-s velocity ratio from compressional p-wave speed and shear s-wave speed.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Seismic P-to-S Wave Velocity Ratio to answer this question: calculate p-to-s velocity ratio from compressional p-wave speed and shear s-wave speed? Enter compressional P-wave speed and shear S-wave speed; the calculator shows P-to-S velocity ratio. For example: compressional P-wave speed=6.2 and shear S-wave speed=3.55 produce P-to-S velocity ratio=1.7464788732394367. The answer tells you P-to-S velocity ratio.

Age 15Explain it to a 15-year-oldConnect it to the formula

The seismic P-to-S ratio compares compressional-wave speed with shear-wave speed in the same material and conditions. This page evaluates the relationship directly. The rule is c=a/b. Its input values are compressional P-wave speed, shear S-wave speed, and the main result is P-to-S velocity ratio. For example: compressional P-wave speed=6.2 and shear S-wave speed=3.55 produce P-to-S velocity ratio=1.7464788732394367.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated seismic p-to-s wave velocity ratio relation over the valid real-number domain stated below. The implemented relation is c=a/b, evaluated from compressional P-wave speed, shear S-wave speed to produce P-to-S velocity ratio. The seismic P-to-S ratio compares compressional-wave speed with shear-wave speed in the same material and conditions. This page evaluates the relationship directly. Use co-located, phase-consistent velocities; fluids do not support an ordinary propagating S wave.

Inputs and valid domain

  • compressional P-wave speed must be a finite real number.
  • shear S-wave speed must be a finite real number.

Important boundary: Use co-located, phase-consistent velocities; fluids do not support an ordinary propagating S wave.

The formula

c=a/b

How the calculator works through it

It substitutes compressional P-wave speed, shear S-wave speed into the formula and exposes every numerical step above. The main output is P-to-S velocity ratio.

Read the result correctly

The P-to-S velocity ratio is the direct answer to “calculate p-to-s velocity ratio from compressional p-wave speed and shear s-wave speed.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

compressional P-wave speed=6.2 and shear S-wave speed=3.55 produce P-to-S velocity ratio=1.7464788732394367.

Where this model stops being reliable

Use co-located, phase-consistent velocities; fluids do not support an ordinary propagating S wave.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Seismic P-to-S Wave Velocity Ratio works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Seismic P-to-S Wave Velocity Ratio uses c=a/b. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

  • Averages and representative values

    Representative values help you judge what the Seismic P-to-S Wave Velocity Ratio inputs summarise and what the result can legitimately describe.

    Review this foundation about 5 min

Optional enrichment

  • Spread and measurement variation

    Variation is not always part of the Seismic P-to-S Wave Velocity Ratio formula, but it helps you judge how stable a reported result may be.

    Review this foundation about 6 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Read compressional P-wave speed, shear S-wave speed.
  2. Evaluate the principal relationship: c=a/b.
  3. Return P-to-S velocity ratio and check the domain conditions described above.
Python
            from math import *

def seismic_p_s_velocity_ratio_calculator(a, b) -> float:
    return (a / b)

assert abs(seismic_p_s_velocity_ratio_calculator(6.2, 3.55) - 1.7464788732394367) < 1e-6 * max(1.0, abs(1.7464788732394367))
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <math.h>

double seismic_p_s_velocity_ratio_calculator(double a, double b) {
    return (a / b);
}

int main(void) {
    const double expected = 1.7464788732394367;
    const double actual = seismic_p_s_velocity_ratio_calculator(6.2, 3.55);
    assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cmath>
#include <numbers>

double seismic_p_s_velocity_ratio_calculator(double a, double b) {
    return (a / b);
}

int main() {
    constexpr double expected = 1.7464788732394367;
    const double actual = seismic_p_s_velocity_ratio_calculator(6.2, 3.55);
    assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · SSE2 with libm where required

            ; double seismic_p_s_velocity_ratio_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global seismic_p_s_velocity_ratio_calculator
section .text

seismic_p_s_velocity_ratio_calculator:
    push rbp
    mov rbp, rsp
    sub rsp, 32
    movsd [rbp-8], xmm0
    movsd [rbp-16], xmm1
    movsd xmm0, [rbp-8]
    divsd xmm0, [rbp-16]
    movsd [rbp-24], xmm0
    movsd xmm0, [rbp-24]
    leave
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = seismic_p_s_velocity_ratio_calculator(a, b)
    result = (a / b);
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / b);
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Introductory Statistics 2e

Read the free OpenStax statistics textbook
Cite this book
APA 7
Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
MLA 9
Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
Chicago author-date
Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Seismic P-to-S Wave Velocity Ratio Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/seismic-p-s-velocity-ratio-calculator

MLA 9

MW SysArc. “Seismic P-to-S Wave Velocity Ratio Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/seismic-p-s-velocity-ratio-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Seismic P-to-S Wave Velocity Ratio Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/seismic-p-s-velocity-ratio-calculator.

Harvard

MW SysArc (2026) ‘Seismic P-to-S Wave Velocity Ratio Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/seismic-p-s-velocity-ratio-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_seismic_p_s_velocity_ratio_calculator_2026,
  author = {{MW SysArc}},
  title = {Seismic P-to-S Wave Velocity Ratio Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/statistics/seismic-p-s-velocity-ratio-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Seismic P-to-S Wave Velocity Ratio Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/statistics/seismic-p-s-velocity-ratio-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Seismic P-to-S Wave Velocity Ratio do?

Calculate p-to-s velocity ratio from compressional p-wave speed and shear s-wave speed.

How does the Seismic P-to-S Wave Velocity Ratio work?

The calculator applies c=a/b. The seismic P-to-S ratio compares compressional-wave speed with shear-wave speed in the same material and conditions. This page evaluates the relationship directly.

What can I learn from the Seismic P-to-S Wave Velocity Ratio?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

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