Calculateus

Coulomb's Law Calculator

Calculate the electrostatic force between two charged particles using Coulomb's Law.

Result

Electrostatic Force
0.2157 N (attractive)

About the Coulomb's Law Calculator

This calculator computes the electrostatic force between two point charges using Coulomb's Law, the fundamental relationship describing how charged particles attract or repel each other. It is useful for physics coursework, circuit design sanity checks, and anyone estimating the force between two known charges at a given separation.

How It Works

You input the two charges in microcoulombs (which can be positive or negative) and the distance between them in meters. The calculator multiplies the charges together, multiplies by Coulomb's constant, and divides by the square of the distance. The sign of the result determines whether the labeled output reads as repulsive or attractive, while the magnitude is reported separately in newtons.

F = k * q1 * q2 / d^2, where k = 8.9875 x 10^9 N*m^2/C^2, and q1, q2 are converted from microcoulombs to coulombs before the calculation

Formula & Methodology

Enter each charge in microcoulombs; the tool internally multiplies by 1e-6 to convert to coulombs before applying the formula. The distance must be in meters and is squared in the denominator, so the force falls off sharply as separation increases. A positive product of q1 and q2 (both charges the same sign) yields a positive force value labeled repulsive, while a negative product (opposite signs) yields a negative value labeled attractive; the displayed magnitude is always the absolute value.

Examples

Opposite charges half a meter apart

With charge 1 at 2 microcoulombs and charge 2 at -3 microcoulombs separated by 0.5 meters, the force works out to about 0.2157 N, and because the charges have opposite signs the calculator labels it attractive.

Two like charges close together

Two charges of 1 microcoulomb each, separated by 0.1 meters, produce a force of roughly 0.899 N. Since both charges share the same sign, the result is labeled repulsive.

Advantages

  • Automatically converts microcoulomb inputs to coulombs, avoiding a common source of order-of-magnitude errors when applying Coulomb's constant
  • Labels the result as attractive or repulsive based on charge signs, removing the need to reason through sign conventions manually
  • Guards against a zero or negative distance input, which would otherwise produce an undefined or nonsensical result

Common Mistakes

  • Forgetting that the input field expects microcoulombs, not coulombs, and entering a raw coulomb value that is far too large
  • Overlooking that the sign of each charge matters for determining attraction versus repulsion, not just the calculated magnitude
  • Using a distance measured in centimeters or millimeters without converting to meters first, which skews the squared denominator

Edge Cases to Watch For

  • If distance is entered as zero or negative, the calculator returns an error instead of dividing by zero or an undefined negative-distance result.
  • The formula treats both charges as point charges with no physical size, so it will overstate force accuracy for charged objects with significant physical extent at close range.
  • Extremely small distances combined with large charges can produce very large force values, since the inverse-square relationship means force grows without bound as separation approaches zero.

Common Use Cases

  • Physics students verifying homework answers on electrostatic force problems
  • Electronics hobbyists estimating forces in capacitor or electrostatic discharge scenarios
  • Educators building example problems with quick, checkable force values
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

How do I know if the force is attractive or repulsive?

Like charges (both positive or both negative) repel, producing a positive force value in the formula; opposite charges attract, producing a negative value - the magnitude of the force follows an inverse-square law with distance, just like gravity, but is vastly stronger at the same distance and mass/charge scale.

Conclusion

Coulomb's Law describes one of the four fundamental forces, and this calculator handles the unit conversion and sign interpretation so the focus stays on the physics. It applies strictly to idealized point charges, so treat results for extended or irregularly shaped charged bodies as approximations.