Mathematics · Mathematical Physics
Radio Effective Isotropic Radiated Power Calculator
Calculate effective isotropic radiated power from transmitter power delivered toward antenna and antenna gain relative to isotropic in linear units.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use c=ab with transmitter power delivered toward antenna=40 and antenna gain relative to isotropic in linear units=12.6.
- effective isotropic radiated power=504.
Understand Radio Effective Isotropic Radiated Power
One idea, three depths
Choose how deeply to explain Radio Effective Isotropic Radiated Power
Radio Effective Isotropic Radiated Power: Calculate effective isotropic radiated power from transmitter power delivered toward antenna and antenna gain relative to isotropic in linear units.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Radio Effective Isotropic Radiated Power to answer this question: calculate effective isotropic radiated power from transmitter power delivered toward antenna and antenna gain relative to isotropic in linear units? Enter transmitter power delivered toward antenna and antenna gain relative to isotropic in linear units; the calculator shows effective isotropic radiated power. For example: transmitter power delivered toward antenna=40 and antenna gain relative to isotropic in linear units=12.6 produce effective isotropic radiated power=504. The answer tells you effective isotropic radiated power.
Age 15Explain it to a 15-year-oldConnect it to the formula
Linear EIRP is transmitter power delivered toward the antenna multiplied by linear antenna gain relative to isotropic. This page evaluates the relationship directly. The rule is c=ab. Its input values are transmitter power delivered toward antenna, antenna gain relative to isotropic in linear units, and the main result is effective isotropic radiated power. For example: transmitter power delivered toward antenna=40 and antenna gain relative to isotropic in linear units=12.6 produce effective isotropic radiated power=504.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated radio effective isotropic radiated power relation over the valid real-number domain stated below. The implemented relation is c=ab, evaluated from transmitter power delivered toward antenna, antenna gain relative to isotropic in linear units to produce effective isotropic radiated power. Linear EIRP is transmitter power delivered toward the antenna multiplied by linear antenna gain relative to isotropic. This page evaluates the relationship directly. Subtract feed and mismatch losses before this product and never multiply by antenna gain expressed in decibels.
Inputs and valid domain
- transmitter power delivered toward antenna must be a finite real number.
- antenna gain relative to isotropic in linear units must be a finite real number.
Important boundary: Subtract feed and mismatch losses before this product and never multiply by antenna gain expressed in decibels.
The formula
c=ab
How the calculator works through it
It substitutes transmitter power delivered toward antenna, antenna gain relative to isotropic in linear units into the formula and exposes every numerical step above. The main output is effective isotropic radiated power.
Read the result correctly
The effective isotropic radiated power is the direct answer to “calculate effective isotropic radiated power from transmitter power delivered toward antenna and antenna gain relative to isotropic in linear units.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
transmitter power delivered toward antenna=40 and antenna gain relative to isotropic in linear units=12.6 produce effective isotropic radiated power=504.
Where this model stops being reliable
Subtract feed and mismatch losses before this product and never multiply by antenna gain expressed in decibels.
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 Radio Effective Isotropic Radiated Power works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Radio Effective Isotropic Radiated Power 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
- Ratios, units and dimensional meaning
Tracking ratios and units keeps the Radio Effective Isotropic Radiated Power result physically interpretable instead of merely numerical.
Review this foundation about 5 min
Optional enrichment
- Vectors and physical direction
Vector language extends Radio Effective Isotropic Radiated Power when magnitude and direction must be treated separately.
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 transmitter power delivered toward antenna, antenna gain relative to isotropic in linear units.
- Evaluate the principal relationship: c=ab.
- Return effective isotropic radiated power and check the domain conditions described above.
Python
from math import *
def radio_effective_isotropic_radiated_power_calculator(a, b) -> float:
return (a * b)
assert abs(radio_effective_isotropic_radiated_power_calculator(40, 12.6) - 504) < 1e-6 * max(1.0, abs(504))
C
#include <assert.h>
#include <math.h>
double radio_effective_isotropic_radiated_power_calculator(double a, double b) {
return (a * b);
}
int main(void) {
const double expected = 504;
const double actual = radio_effective_isotropic_radiated_power_calculator(40, 12.6);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double radio_effective_isotropic_radiated_power_calculator(double a, double b) {
return (a * b);
}
int main() {
constexpr double expected = 504;
const double actual = radio_effective_isotropic_radiated_power_calculator(40, 12.6);
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 radio_effective_isotropic_radiated_power_calculator(double a, double b)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global radio_effective_isotropic_radiated_power_calculator
section .text
radio_effective_isotropic_radiated_power_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 = radio_effective_isotropic_radiated_power_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.
University Physics Volume 3
Read OpenStax University Physics: Quantum MechanicsCite this book
- APA 7
- Ling, S. J., Sanny, J., & Moebs, W. (2016). University physics volume 3. OpenStax. https://openstax.org/books/university-physics-volume-3/pages/1-introduction
- MLA 9
- Ling, Samuel J., et al. University Physics Volume 3. OpenStax, 2016, https://openstax.org/books/university-physics-volume-3/pages/1-introduction.
- Chicago author-date
- Ling, Samuel J., Jeff Sanny, and William Moebs. 2016. University Physics Volume 3. Houston, TX: OpenStax. https://openstax.org/books/university-physics-volume-3/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). Radio Effective Isotropic Radiated Power Calculator. MW SysArc Tools. https://math.mwsysarc.com/mathematical-physics/radio-effective-isotropic-radiated-power-calculator
MLA 9
MW SysArc. “Radio Effective Isotropic Radiated Power Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/mathematical-physics/radio-effective-isotropic-radiated-power-calculator. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Radio Effective Isotropic Radiated Power Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/mathematical-physics/radio-effective-isotropic-radiated-power-calculator.
Harvard
MW SysArc (2026) ‘Radio Effective Isotropic Radiated Power Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/mathematical-physics/radio-effective-isotropic-radiated-power-calculator (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_radio_effective_isotropic_radiated_power_calculator_2026,
author = {{MW SysArc}},
title = {Radio Effective Isotropic Radiated Power Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/mathematical-physics/radio-effective-isotropic-radiated-power-calculator},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Radio Effective Isotropic Radiated Power Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/mathematical-physics/radio-effective-isotropic-radiated-power-calculator
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Radio Effective Isotropic Radiated Power do?
Calculate effective isotropic radiated power from transmitter power delivered toward antenna and antenna gain relative to isotropic in linear units.
How does the Radio Effective Isotropic Radiated Power work?
The calculator applies c=ab. Linear EIRP is transmitter power delivered toward the antenna multiplied by linear antenna gain relative to isotropic. This page evaluates the relationship directly.
What can I learn from the Radio Effective Isotropic Radiated Power?
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 .