# Coulomb's Law Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jul 07, 2023

This electric force calculator will enable you to determine the repulsive or attractive force between two static charged particles. Continue reading to get a better understanding of Coulomb's law, the conditions of its validity, and the physical interpretation of the obtained result.

## How to use Coulomb's law

Coulomb's law, otherwise known as Coulomb's inverse-square law, describes the electrostatic force acting between two charges. The force acts along the shortest line that joins the charges. It is repulsive if both charges have the same sign and attractive if they have opposite signs.

Coulomb's law is formulated as follows:

$F = \frac{\mathrm{k_e} q_1 q_2}{r^2}$

where:

• $F$ is the electrostatic force between charges (in Newtons),
• $q_1$ is the magnitude of the first charge (in Coulombs),
• $q_2$ is the magnitude of the second charge (in Coulombs),
• $r$ is the shortest distance between the charges (in m),
• $\mathrm{k_e}$ is the Coulomb's constant. It is equal to $8.98755 \cdot 10^9 \ \mathrm{\frac{N\cdot m^2}{C^2}}$. This value is already embedded in the calculator - you don't have to remember it :)

Simply input any three values into our electric force calculator to obtain the fourth as a result.

To compute the electric potential at a point either due to a single point charge or a system of point charges, check out our electric potential calculator. We've also got the electric field calculator for point charges.

## Electric charge units

The unit of electric charge is a Coulomb (symbol: C). It is defined as the charge that is transported by a constant current of 1 ampere during 1 second. Hence, $\mathrm{1 \ C = 1 \ A \cdot 1 \ s}$ expressed in SI units.

If you don't remember what an ampere is, head to our Ohm's law calculator.

## Conditions for validity

Three main conditions must be fulfilled for the electrostatic force calculator to return valid values:

1. Charges must be stationary - they cannot move with respect to each other.
2. Point charges are assumed. This assumption also holds for any charges that are spherical and symmetric. For example, a charged metal sphere fulfills this condition, but a charged metal box doesn't.
3. Charges cannot overlap - they must be distinct and have at least a minimal distance between them.

## Interpretation of results

Force obtained with the help of our Coulomb's law calculator can be either positive or negative. Positive force implies a repulsive interaction between the charges. Negative force means that the interaction is attractive.

Did you notice that the default unit for charge in our Coulomb's law calculator is a nanoCoulomb (nC)? It is because the typical order of magnitude of an electric charge is $\mathrm{10^{-6} \ C}$ or even $\mathrm{10^{-9} \ C}$.

## FAQ

### How do I calculate the force between two charged particles?

To calculate the force between two charged particles, we use the Coulomb's law. Follow these easy steps to find the result:

1. Find the charges q1 and q2 of the particles in coulombs, and multiply them.
2. Multiply the result of step 1. by the constant ke = 8.988E9 (N × m²)/C².
3. Divide the result by the square of the distance between the particles.

The result is the force (attractive if negative in sign, repulsive if positive) acting between the charged particles.

### Is the Coulomb's law an inverse square law?

The presence of the square of the distance between two particles at the denominator of the formula of Coulomb's law makes it an inverse square law. This property stems from the point nature of the electric charge considered in the formula: since the electric field emanates radially, the field spreads on the surface of a sphere, which is equal to 4 × π × r². In the case of Coulomb's law, experimental results confirm this finding stating that the exponent is 2, and the next 15 decimal places are filled with zeros!

### What is the force between a proton and an electron in a hydrogen atom?

The force of attraction between an electron and a proton in a hydrogen atom is 1.60E-8 N. To find this result, start by laying down the known data:

1. The charge of an electron and a proton is the same, with opposite sign, and equal to qe = -qp = -1.602176634E-19 C.
2. The distance between electron and proton in a hydrogen atom is approximately 0.120 nm = 120E-12 m.
3. Find the force with the following formula:
F = ke × qe × qp/r² = - 8.988E9 × (1.602176634E-19)²/(120E-12)² = 1.60E-8 N

### Is Coulomb's force attractive or repulsive?

The effect of Coulomb's force on electric charges depends on their sign. While gravity acts only as an attractive force, the possible combinations of signs of the charges make Coulomb's force either repulsive or attractive:

• If both charges have the same sign, Coulomb's force is repulsive;
• If the charges have opposite sign, Coulomb's force is attractive.

This different nature is among the thing that permits the existence of atoms!

Bogna Szyk Charges are...
not equal
Charge 1 (q₁)
nC
Charge 2 (q₂)
nC
Distance (r)
mm
Force (F)
lbf
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