Coulombs Law Calculator

Introduction

Coulomb’s law states that the magnitude of electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Using our Coulombs law calculator, you can calculate either the force of attraction or repulsion between those charges.

The force acting on the two-point charges will act along the straight line, joining the two charges. If the charges have the same sign, then the electrostatic force between them is repulsive, and if they have different signs, the force between them is attractive.

How to use the Coulombs Law Calculator?

Using the Coulombs law calculator, you can calculate the force of attraction or repulsion between two stationary and electrically charged particles.

The variables in the calculator include

Charge (q1) The amount of charge on particle 1

Charge (q2) The amount of charge on particle 2

Distance (r) The distance between the two charges

Coulomb Constant (ke) The Coulomb’s constant is also called the electric force or electrostatic constant. It is given by the following equation

K_e = \dfrac{1}{4 \pi\epsilon_0}

Where,

ε0 → is the vacuum electric permittivity

We consider the value of coulomb’s constant as

8.9875517923 (14) x 10^9 N m^2 C^-2

Electric Force (F) The electric force between two point charges, given by the formula

F = \dfrac{k_e \cdot| q_1 |\cdot |q_2| }{r^2}

What is Coulomb’s Law?

Coulomb’s law states that the magnitude of electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Also, the force will act along the straight line joining the two charges.

If the charges have the same sign, then the electrostatic force between them is repulsive, and if they have different signs, the force between them is attractive.

A French physicist, Charles Augustin de Coulomb, studied the interaction forces of charged particles around 1784 and came up with a theory for the electrostatic force between charged objects.

Coulomb used a torsion balance to study the strength of the forces between charged particles. It is an insulating rod with a metal-coated ball attached to one end suspended by a very thin silk thread. The ball was electrostatically charged, and when a second ball which is also electrostatically charged with the same polarity, was brought near it due to the repulsive force of the fiber, it made a certain angle with the rod. So, Coulomb could measure the force required to push the ball to make the angle.

In 1785, he published three reports on electricity and magnetism, stating the law. Subsequently, Coulomb’s law was essential to the development of the theory of electromagnetism.

How is the Electric Force Between two charged particles calculated?

The magnitude of the electrostatic force between two stationary point charges is given by the following equation

F = \dfrac{k_e \cdot| q_1 |\cdot |q_2| }{r^2}

Where,

q1 → The charge on particle 1

q2 → The charge on particle 2

r → the distance between the two particles

ke → the proportionality constant, the value is 8.987551787 * 10^9 N m^2/C^2

ke is given by the following formula

K_e = \dfrac{1}{4 \pi\epsilon_0}

Where,

ε0 → is the vacuum electric permittivity, it value is 8.854 x 10^(-12) C^2/N m^2

Together, we can write the entire equation as shown below

F = \dfrac{1}{4 \pi\epsilon_0} \cdot \dfrac{| q_1 |\cdot |q_2| }{r^2}

Examples

Given, two point charges, q1 = 30 nC and q2 = 60 nC, are separated by a distance of 2 cm. What is the magnitude of the electric force?

\begin{aligned} F &= \dfrac{1}{4 \pi\epsilon_0} \cdot \dfrac{| q_1 |\cdot |q_2| }{r^2} \\[10pt] &= \dfrac{1}{4 \pi \; 8.854 \times 10^{-12}C^2/N \cdot m^2} \cdot \dfrac{| 30 \times 10^{-9}C |\cdot |60 \times 10^{-9}C| }{0.02^2} \\[10pt] &= 8.988 \times 10^9 N \cdot m^2/C^2 \cdot 4.5 \; C^2/m^2 \times 10^{-12} \\[10pt] &= 0.040446 \; N \end{aligned}

Applications of Coulomb's Law

Coulomb's law underpins a surprisingly wide range of everyday and scientific phenomena. Inside every atom it binds negatively charged electrons to the positively charged nucleus, which in turn shapes how atoms join to form molecules and chemical bonds.

On a larger scale, the same law explains how electrostatic precipitators in power plants pull ash and dust particles from flue gases by giving them a charge and attracting them to oppositely charged plates. Photocopiers and laser printers use a charged drum to attract toner particles to the right spots on paper, while capacitors in electronics store energy in the form of charge separation governed by Coulomb forces. Even the static shock you feel after walking on a carpet is just Coulomb's law at work between you and a nearby door handle.

Tips and Common Mistakes

A few small slip-ups account for most wrong answers when using Coulomb's law. Keep these in mind:

Convert charge units carefully — values are usually given in nanocoulombs (nC = 10⁻⁹ C) or microcoulombs (µC = 10⁻⁶ C). Plugging in the prefixed number without the power of ten can throw the result off by many orders of magnitude.

Square the distance, don't just use it — the force falls off with r², not r. Doubling the distance cuts the force to one-quarter, not one-half.

Mind the sign convention — if you enter signed charges, a negative product (opposite signs) yields an attractive force (negative F by convention) and a positive product (same signs) yields a repulsive force. If you only care about magnitude, use the absolute values of q₁ and q₂.

Stick to SI when in doubt — coulombs for charge, meters for distance, newtons for force. The Coulomb constant kₑ ≈ 8.99 × 10⁹ N·m²/C² is already baked into this calculator, so you only need to focus on entering consistent units.

FAQs

How is Coulomb’s Law used in physics?

Coulomb’s Law is used in electricity, magnetism, and other fields such as chemical bonding and nuclear physics.

How does Coulomb’s Law relate to electric fields?

Coulomb’s Law is closely related to the concept of electric fields. In essence, an electric field is defined as the force experienced per unit charge. Also, the force exerted in an electric field is directly proportional to the magnitude of the test charge and the strength of the electric field.

How does Coulomb’s Law relate to charges?

Coulomb’s Law describes the interaction between charges, and it also states that charges of the same sign will repel each other, and charges of opposite signs will attract each other.

Does Coulomb’s Law apply to all types of charges?

Coulomb’s Law applies to all types of charges, whether positive or negative, as long as they are point charges. However, it does not apply to charges distributed over a surface and moving with respect to each other.

How is Coulomb's law different from Newton's law of gravitation?

Both laws share the same inverse-square form, but Coulomb's law deals with electric charges and can be either attractive or repulsive depending on the sign of the charges, while Newton's law of gravitation deals with masses and is always attractive. Electric forces are also enormously stronger than gravitational forces between elementary particles — roughly 10³⁶ times stronger for two electrons.

Why does the force follow an inverse-square law?

Imagine the electric influence of a point charge spreading outward equally in every direction, like light from a tiny bulb. At a distance r, that influence is distributed over the surface of a sphere of area 4πr². As r grows, the same total "flux" is spread over a larger and larger surface, so the strength at any one point drops in proportion to 1/r². This is the same geometric reason that gravity, sound, and light intensity all follow inverse-square laws.

When does Coulomb's law break down?

Coulomb's law in its simple form assumes point charges that are stationary (or moving slowly) and located in a vacuum or uniform medium. It becomes inaccurate when charges are moving fast enough for magnetic and relativistic effects to matter, when they are extended objects with non-uniform charge distributions, or when the surrounding material is polarizable (in which case the constant kₑ is replaced by 1/(4πε), where ε accounts for the medium). At very small (subatomic) distances, quantum electrodynamics replaces the classical picture entirely.