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.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=a/b with compressional P-wave speed=6.2 and shear S-wave speed=3.55.
- 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
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
- Read compressional P-wave speed, shear S-wave speed.
- Evaluate the principal relationship: c=a/b.
- 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))
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)));
}
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)));
}
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
MATLAB
function result = seismic_p_s_velocity_ratio_calculator(a, b)
result = (a / b);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_] := (a / b);
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 textbookCite 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 .