Boneyard Tools

Understanding Coulomb's law and electric force

What each term in Coulomb's law means, how the inverse-square distance shapes the force, and how to enter charges in coulombs correctly.

Open the Coulomb's Law Calculator →

The equation term by term

Coulomb's law reads F equals k times q1 times q2 divided by r squared, and this tool reports the magnitude using the absolute value of the charge product. The symbol k is the Coulomb constant, roughly 8.9875 billion newton metres squared per coulomb squared, which sets the overall strength of the interaction. The charges q1 and q2 are measured in coulombs, and r is the distance between the two point charges in metres. The sign of the product q1 times q2 decides direction: negative means the charges attract, positive means they repel.

Why distance matters so much

Because the separation appears as r squared in the denominator, the force falls off steeply as the charges move apart. Doubling the distance cuts the force to a quarter, and tripling it drops the force to a ninth. Conversely, halving the gap makes the force four times as strong, which is why the closer, larger charges example jumps to about 21.57 newtons. This sharp dependence is the same inverse-square pattern seen in gravity and in the brightness of light.

Entering charges in coulombs

A coulomb is a very large amount of charge, so real problems almost always use fractions of one. Scientists write these with scientific notation, and the calculator accepts that directly: 1e-6 is one microcoulomb, 1e-9 is one nanocoulomb, and 1e-12 is one picocoulomb. Add a minus sign in front to make a charge negative, for instance -2e-6 for a negative two microcoulomb charge. Mixing a positive and a negative charge is how you model attraction between unlike bodies.

Where the numbers come from in practice

Static electricity on a balloon might carry a few tens of nanocoulombs, while a capacitor plate could hold microcoulombs. The elementary charge on a single electron or proton is about 1.6 x 10^-19 coulombs, so bulk objects contain astronomical numbers of them. Because the constant k is so large, even modest charges separated by short distances can produce forces you can feel, which is the basis of many electrostatics demonstrations.

Frequently asked questions

Does the order of the two charges matter?

No. Because the formula multiplies the two charges together, swapping Charge 1 and Charge 2 gives the same magnitude and the same attract-or-repel label. Only the signs and the distance change the outcome.

What happens if one charge is zero?

The force is zero, since multiplying by a zero charge removes the product entirely. The calculator reports 0 N and treats the pair as neither attractive nor repulsive.

Is Coulomb's law exact for real objects?

It is exact for ideal point charges and an excellent approximation for small charged bodies that are far apart compared with their size. For large or oddly shaped conductors the charge spreads out, and you would integrate the law over the distribution for a precise answer.