Mathematics · Trigonometry
Periodic Sample Phase Calculator
Calculate sample phase from sample index and phase increment per sample.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=ab with sample index=24 and phase increment per sample=0.15.
- sample phase=3.5999999999999996.
Understand Periodic Sample Phase
One idea, three depths
Choose how deeply to explain Periodic Sample Phase
Periodic Sample Phase: Calculate sample phase from sample index and phase increment per sample.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Periodic Sample Phase to answer this question: calculate sample phase from sample index and phase increment per sample? Enter sample index and phase increment per sample; the calculator shows sample phase. For example: sample index=24 and phase increment per sample=0.15 produce sample phase=3.5999999999999996. The answer tells you sample phase.
Age 15Explain it to a 15-year-oldConnect it to the formula
Uniformly sampled phase equals sample index multiplied by phase increment. This page evaluates the relationship directly. The rule is c=ab. Its input values are sample index, phase increment per sample, and the main result is sample phase. For example: sample index=24 and phase increment per sample=0.15 produce sample phase=3.5999999999999996.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated periodic sample phase relation over the valid real-number domain stated below. The implemented relation is c=ab, evaluated from sample index, phase increment per sample to produce sample phase. Uniformly sampled phase equals sample index multiplied by phase increment. This page evaluates the relationship directly. Add initial phase separately and use a consistent zero- or one-based index convention.
Inputs and valid domain
- sample index must be a finite real number.
- phase increment per sample must be a finite real number.
Important boundary: Add initial phase separately and use a consistent zero- or one-based index convention.
The formula
c=ab
How the calculator works through it
It substitutes sample index, phase increment per sample into the formula and exposes every numerical step above. The main output is sample phase.
Read the result correctly
The sample phase is the direct answer to “calculate sample phase from sample index and phase increment per sample.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
sample index=24 and phase increment per sample=0.15 produce sample phase=3.5999999999999996.
Where this model stops being reliable
Add initial phase separately and use a consistent zero- or one-based index convention.
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 Periodic Sample Phase works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Periodic Sample Phase uses c=ab. 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
- Angles in degrees and radians
Interpreting the angle convention is essential for understanding the inputs and output of Periodic Sample Phase.
Review this foundation about 5 min
Optional enrichment
- Functions and their graphs
Function graphs show how the Periodic Sample Phase relationship changes across a full angle or period.
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 sample index, phase increment per sample.
- Evaluate the principal relationship: c=ab.
- Return sample phase and check the domain conditions described above.
Python
from math import *
def periodic_sample_phase_calculator(a, b) -> float:
return (a * b)
assert abs(periodic_sample_phase_calculator(24, 0.15) - 3.5999999999999996) < 1e-6 * max(1.0, abs(3.5999999999999996))
C
#include <assert.h>
#include <math.h>
double periodic_sample_phase_calculator(double a, double b) {
return (a * b);
}
int main(void) {
const double expected = 3.5999999999999996;
const double actual = periodic_sample_phase_calculator(24, 0.15);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double periodic_sample_phase_calculator(double a, double b) {
return (a * b);
}
int main() {
constexpr double expected = 3.5999999999999996;
const double actual = periodic_sample_phase_calculator(24, 0.15);
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 periodic_sample_phase_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global periodic_sample_phase_calculator
section .text
periodic_sample_phase_calculator:
push rbp
mov rbp, rsp
sub rsp, 32
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = periodic_sample_phase_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.
Algebra and Trigonometry 2e
Read the related free OpenStax mathematics chaptersCite this book
- APA 7
- Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
- MLA 9
- Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
- Chicago author-date
- Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
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). Periodic Sample Phase Calculator. MW SysArc Tools. https://math.mwsysarc.com/trigonometry/periodic-sample-phase-calculator
MLA 9
MW SysArc. “Periodic Sample Phase Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/trigonometry/periodic-sample-phase-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Periodic Sample Phase Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/trigonometry/periodic-sample-phase-calculator.
Harvard
MW SysArc (2026) ‘Periodic Sample Phase Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/trigonometry/periodic-sample-phase-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_periodic_sample_phase_calculator_2026,
author = {{MW SysArc}},
title = {Periodic Sample Phase Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/trigonometry/periodic-sample-phase-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Periodic Sample Phase Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/trigonometry/periodic-sample-phase-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Periodic Sample Phase do?
Calculate sample phase from sample index and phase increment per sample.
How does the Periodic Sample Phase work?
The calculator applies c=ab. Uniformly sampled phase equals sample index multiplied by phase increment. This page evaluates the relationship directly.
What can I learn from the Periodic Sample Phase?
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 .