Electric Force Against Gravity Calculator: How Much Stronger Is Coulomb's Force
How much stronger the electric force is than gravity between two bodies.
Engineering student calculators
Free textbook calculators with every step shown, so you can check your own working. Pick one, type in your numbers and see the formulas worked out. Or switch to Ask a question for an explained answer. No account needed.
Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.
How this calculator works
Choose two protons, two electrons, a proton and an electron, or enter your own charges and masses.
Enter the distance between the centres. The ratio does not depend on it, but the two forces do.
The calculator gives the electric force, the gravitational force and the ratio of one to the other.
Formulas used
- F_e = k\frac{q_1q_2}{r^2}
- F_g = G\frac{m_1m_2}{r^2}
- \frac{F_e}{F_g} = \frac{k\,q_1q_2}{G\,m_1m_2}
Worked example
With the default numbers in the calculator above:
- Charges and masses used: two protons
- Electric force: 2.3071e-28 N
- Gravitational force: 1.8672e-64 N
- Ratio of the electric force to the gravitational force: 1.2356e+36
- Ratio of the gravitational force to the electric force: 8.0936e-37
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: Which bodies? Two electrons.
- Charges and masses used: two electrons
- Electric force: 2.3071e-28 N
- Gravitational force: 5.5384e-71 N
- Ratio of the electric force to the gravitational force: 4.1656e+42
- Ratio of the gravitational force to the electric force: 2.4006e-43
Common questions
How much stronger is the electric force than gravity?
Between two protons the electric force is about 1.24 times 10 to the power 36 stronger than gravity. Between two electrons it is about 4.17 times 10 to the power 42.
Why does the distance not change the ratio?
Both forces fall off with the square of the distance, so it cancels when you divide one by the other.
Why does gravity win for planets?
Charge comes in both signs and cancels, so large objects are nearly neutral. Mass only ever adds, and it cannot be shielded.
What constants does it use?
The exact values k = 8.9876 x 10^9 N m2/C2 and G = 6.6743 x 10^-11 N m2/kg2, or the rounded textbook values 8.99 x 10^9 and 6.67 x 10^-11 if you choose them.
Related calculators
Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any physics text (Coulomb's law and Newton's law of gravitation).
Need a calculator we do not have?
Embed this calculator on your own page
Copy this code into your page. The calculator runs inside the frame and links back to Drafting Central.
Need this drawn, designed or checked?
Drafting Central is a mechanical engineering and drafting business working with customers across Australia and around the world. A calculator gives you the numbers; we can turn them into drawings and designs.
Need help with a real project?
Talk to Drafting Central →