Mathematics · Mathematical Physics
Universal Gravitational Force Calculator
Calculate Newtonian gravitational attraction between two point masses.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Mass product=1000×1000=1000000.
- Distance squared=2²=4.
- Force=6.6743e-11×1000000÷4=0.00001668575 N.
Understand Gravitational force
One idea, three depths
Choose how deeply to explain Gravitational force
Gravitational force: Calculate Newtonian gravitational attraction between two point masses.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Gravitational force to answer this question: calculate newtonian gravitational attraction between two point masses? Enter First mass m₁, Second mass m₂, Separation r; the calculator shows Gravitational force. For example: Two 1000 kg masses 2 m apart attract with approximately 1.6686×10⁻⁵ N. The answer tells you Gravitational force.
Age 15Explain it to a 15-year-oldConnect it to the formula
Gravity grows with both masses and decreases with the square of their centre-to-centre separation. The rule is F=Gm₁m₂/r². Its input values are First mass m₁ (kg), Second mass m₂ (kg), Separation r (m), and the main result is Gravitational force. For example: Two 1000 kg masses 2 m apart attract with approximately 1.6686×10⁻⁵ N.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated gravitational force relation over the valid real-number domain stated below. The implemented relation is F=Gm₁m₂/r², evaluated from First mass m₁ (kg), Second mass m₂ (kg), Separation r (m) to produce Gravitational force. Gravity grows with both masses and decreases with the square of their centre-to-centre separation. Use centre-to-centre distance and SI units when using the displayed gravitational constant.
Inputs and valid domain
- First mass m₁ must be a finite real number, at least 0 in kg.
- Second mass m₂ must be a finite real number, at least 0 in kg.
- Separation r must be a finite real number, at least 0 in m.
Important boundary: Use centre-to-centre distance and SI units when using the displayed gravitational constant.
The formula
F=Gm₁m₂/r²
How the calculator works through it
It substitutes First mass m₁, Second mass m₂, Separation r into the formula and exposes every numerical step above. The main output is Gravitational force, accompanied by Mass product, Distance squared.
Read the result correctly
The Gravitational force is the direct answer to “calculate newtonian gravitational attraction between two point masses.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
Two 1000 kg masses 2 m apart attract with approximately 1.6686×10⁻⁵ N.
Where this model stops being reliable
Use centre-to-centre distance and SI units when using the displayed gravitational constant.
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 Gravitational force works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Gravitational force uses F=Gm₁m₂/r². 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 Gravitational force result physically interpretable instead of merely numerical.
Review this foundation about 5 min
Optional enrichment
- Vectors and physical direction
Vector language extends Gravitational force 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 First mass m₁, Second mass m₂, Separation r.
- Evaluate the principal relationship: F=Gm₁m₂/r².
- Return Gravitational force and check the domain conditions described above.
Python
from math import *
def universal_gravitation(a, b, r) -> float:
return ((6.6743e-11 * (a * b)) / (r * r))
assert abs(universal_gravitation(1000, 1000, 2) - 0.00001668575) < 1e-6 * max(1.0, abs(0.00001668575))
C
#include <assert.h>
#include <math.h>
double universal_gravitation(double a, double b, double r) {
return ((6.6743e-11 * (a * b)) / (r * r));
}
int main(void) {
const double expected = 0.00001668575;
const double actual = universal_gravitation(1000, 1000, 2);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double universal_gravitation(double a, double b, double r) {
return ((6.6743e-11 * (a * b)) / (r * r));
}
int main() {
constexpr double expected = 0.00001668575;
const double actual = universal_gravitation(1000, 1000, 2);
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 universal_gravitation(double a, double b, double r)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
global universal_gravitation
section .text
universal_gravitation:
push rbp
mov rbp, rsp
sub rsp, 64
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
movsd [rbp-24], xmm2
mov rax, 0x3dd2589effed8acc
movq xmm0, rax
movsd [rbp-48], xmm0
movsd xmm0, [rbp-8]
mulsd xmm0, [rbp-16]
movsd [rbp-56], xmm0
movsd xmm0, [rbp-48]
mulsd xmm0, [rbp-56]
movsd [rbp-40], xmm0
movsd xmm0, [rbp-24]
mulsd xmm0, [rbp-24]
movsd [rbp-64], xmm0
movsd xmm0, [rbp-40]
divsd xmm0, [rbp-64]
movsd [rbp-32], xmm0
movsd xmm0, [rbp-32]
leave
ret
MATLAB
function result = universal_gravitation(a, b, r)
result = ((6.6743e-11 * (a * b)) / (r * r));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[a_, b_, r_] := ((6.6743e-11 * (a * b)) / (r * r));
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). Universal Gravitational Force Calculator. MW SysArc Tools. https://math.mwsysarc.com/mathematical-physics/universal-gravitation
MLA 9
MW SysArc. “Universal Gravitational Force Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/mathematical-physics/universal-gravitation. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Universal Gravitational Force Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/mathematical-physics/universal-gravitation.
Harvard
MW SysArc (2026) ‘Universal Gravitational Force Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/mathematical-physics/universal-gravitation (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_universal_gravitation_2026,
author = {{MW SysArc}},
title = {Universal Gravitational Force Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/mathematical-physics/universal-gravitation},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Universal Gravitational Force Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/mathematical-physics/universal-gravitation
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Gravitational force do?
Calculate Newtonian gravitational attraction between two point masses.
How does the Gravitational force work?
The calculator applies F=Gm₁m₂/r². Gravity grows with both masses and decreases with the square of their centre-to-centre separation.
What can I learn from the Gravitational force?
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 .