Gravitational Force Calculator
Compute gravity between two bodies from their masses and separation. Choose units for each input; get force, conversions, and clear step-by-step work.
Equation Preview
Helping Notes
- Newton’s law: \(F = G\,\dfrac{m_1 m_2}{r^2}\). Only \(m_1, m_2, r\) are needed; \(G\) is a constant.
- Use center-to-center distance. Conversions handled from your selected units to SI (kg and m).
- Constants used: \(G=6.67430×10^{-11}\ \mathrm{m^3\,kg^{-1}\,s^{-2}}\); \(M_{\oplus}\approx5.972×10^{24}\ \mathrm{kg}\); \(M_{\odot}\approx1.988×10^{30}\ \mathrm{kg}\); \(R_{\oplus}\approx6.371×10^6\ \mathrm{m}\); \(R_{\odot}\approx6.957×10^8\ \mathrm{m}\); \(1\ \mathrm{au}=149\,597\,870\,700\ \mathrm{m}\).
Results
Gravitational Force (N)
Conversions
Error
Steps
What is Gravitational Force Calculator?
A Gravitational Force Calculator evaluates the mutual attraction between two masses according to Newton’s law of universal gravitation. Given masses \(m_1\) and \(m_2\) separated by center‑to‑center distance \(r\), the magnitude of the force is proportional to the product of the masses and inversely proportional to the square of the distance. The force is always attractive and acts along the line joining the centers. Near a planet’s surface this reduces to the familiar weight relation \(W=mg\), with \(g\) determined by the planet’s mass and radius. Key formulas are displayed below for quick reference.
About the Gravitational Force Calculator
Enter any two or more known quantities—masses, separation, local \(g\), or a target force—and the calculator solves for the unknowns while showing each algebraic step. It supports magnitude‑only problems and vector problems using coordinates for both bodies. Built‑in options include common celestial bodies (Earth, Moon, Mars) for quick lookup of \(g\) or \(GM\). Unit handling is explicit: you may work in SI (kg, m, N) or in mixed units so long as inputs are consistent. The interface flags impossible inputs like \(r\le0\) or negative masses and reminds you to use center‑to‑center distances for extended objects.
How to Use this Gravitational Force Calculator
- Select mode: Universal law (\(m_1,m_2,r\)) or Weight (\(m,g\)).
- Enter known values and units; choose a body preset if helpful (auto‑fills \(g\) or \(GM\)).
- Click calculate to compute \(F\) and, in vector mode, \(\mathbf F\) components.
- Review the responsive formulas and intermediate steps; adjust inputs to explore sensitivity to \(r\) or mass.
- Copy the results for reports, labs, or homework solutions.
Examples
Example 1: Two lab masses
\(m_1=5\,\text{kg},\; m_2=5\,\text{kg},\; r=0.50\,\text{m}\).
Example 2: Person’s weight on Earth
\(m=80\,\text{kg}\) and \(g\approx9.81\,\text{m/s}^2\).
Example 3: Satellite at 400 km altitude
\(m=500\,\text{kg},\; r=R_E+400\,\text{km}\). Using \(g(r)=g_0(R_E/r)^2\) with \(g_0=9.81\,\text{m/s}^2\).
Example 4: Solve for distance from force
Rearrange Newton’s law to find \(r\) given \(F\), \(m_1\), and \(m_2\).
FAQs
What distance should I use in the formula?
Always use center‑to‑center separation between masses, not surface‑to‑surface distance.
Why is there a minus sign in the vector form?
It indicates attraction: the force on each mass points toward the other along the line connecting them.
How is weight related to gravitational force?
Weight is the gravitational force from a planet on a mass: \(W=mg\) with \(g=GM/R^2\).
Do I need SI units?
SI is recommended (kg, m, N). Mixed units work if you convert consistently before applying the formulas.
Does altitude change my weight?
Yes. \(g\) decreases with \(r\) as \(\propto1/r^2\), so weight is slightly less at higher elevations and in orbit.
Can the calculator handle vector components?
Yes. Provide coordinates for both masses to obtain \(\mathbf F\) components and magnitude.
What about air resistance?
Air resistance affects motion, not the gravitational force itself. The formulas here describe the gravitational interaction only.
Can masses be negative?
No in classical physics. Use nonnegative masses; negative inputs are rejected as unphysical.
How accurate are presets for celestial bodies?
They use standard constants; results are accurate for most purposes. Extreme precision may require local variations in \(g\).