Coulomb's Law Calculator
Enter any three of the four variables - charge 1, charge 2, distance, and electrostatic force - and this calculator instantly solves for the missing one using Coulomb's Law. Choose your preferred units for each quantity, flip between solving for force, distance, or charge, and see the full worked calculation below the result. Positive force means repulsion (same-sign charges), negative means attraction (opposite-sign charges).
Formula
Worked example
Two charges of +1 nC and +2 nC are separated by 0.1 m. F = (8.988 x 10^9) * (1 x 10^-9) * (2 x 10^-9) / (0.1)^2 = (8.988 x 10^9 * 2 x 10^-18) / 0.01 = 1.798 x 10^-6 N (repulsive, same-sign charges).
What is Coulomb's Law?
Coulomb's Law quantifies the electrostatic force between two electrically charged point objects. Published by French physicist Charles-Augustin de Coulomb in 1785, it states that the force is directly proportional to the product of the two charge magnitudes and inversely proportional to the square of the distance between them. The formula is F = k_e * q1 * q2 / r^2, where k_e is Coulomb's constant (8.988 x 10^9 N*m^2/C^2). A positive result means repulsive force (same-sign charges push apart), while a negative result means attractive force (opposite-sign charges pull together). The inverse-square relationship means doubling the separation reduces the force to one-quarter of its original value.
Solving for force, charge, or distance
The law can be rearranged to find any one of its four quantities when the other three are known. To find force: F = k_e * q1 * q2 / r^2. To find an unknown charge: q1 = F * r^2 / (k_e * q2). To find distance: r = sqrt(|k_e * q1 * q2 / F|). When solving for distance, the absolute value is taken inside the square root because distance is always positive - the sign of force (and therefore the direction of interaction) is determined by the charge signs, not the separation. Use the 'Solve for' dropdown at the top to switch modes.
Where Coulomb's Law applies and where it breaks down
Coulomb's Law gives exact results only for point charges (or perfectly spherical, uniformly charged objects) that are stationary relative to each other and surrounded by vacuum. For charges in a dielectric material such as water or glass, divide the vacuum force by the relative permittivity of that medium (water has permittivity of about 80, reducing the force by a factor of 80). At separations approaching the atomic scale, quantum effects become significant. The law also does not directly account for moving charges, whose interactions require the full Maxwell equations including magnetic effects. For most introductory and practical problems involving static charge distributions, Coulomb's Law is the correct starting point.
Coulomb constant and permittivity of free space
Coulomb's constant k_e equals 1 / (4 * pi * epsilon_0), where epsilon_0 is the permittivity of free space (8.854 x 10^-12 F/m). The exact SI value is k_e = 8.9875517923 x 10^9 N*m^2/C^2. The elementary charge e = 1.602176634 x 10^-19 C (exact under the 2019 SI redefinition). These constants are built into this calculator so you only need to enter the charge magnitudes and separation distance. For reference, relative permittivities of common media: vacuum = 1.000, dry air = 1.0006, glass = 4 to 10, water = approximately 80.
Common charge magnitudes
| Particle or Object | Charge (C) | Notes |
|---|---|---|
| Electron | -1.602 x 10^-19 | Elementary negative charge |
| Proton | +1.602 x 10^-19 | Elementary positive charge |
| Alpha particle | +3.204 x 10^-19 | Two protons (fully ionized helium) |
| Typical lab charge | 1 nC to 1 uC | Van de Graaff generator experiments |
| Static shock on skin | ~1 uC | Triboelectric charging |
| Lightning bolt | ~5 C | Typical cloud-to-ground discharge |
| 1 Coulomb | 1 | SI base unit = 6.24 x 10^18 elementary charges |
Representative charge values in physics problems and real-world applications.
Frequently asked questions
What does a negative force mean in Coulomb's Law?
A negative force value means the force is attractive: the two charges have opposite signs (one positive, one negative) and they pull toward each other. A positive force value means repulsion: both charges have the same sign and they push each other apart. The magnitude (absolute value) tells you the strength; the sign tells you the direction.
What is Coulomb's constant and where does it come from?
Coulomb's constant k_e = 8.988 x 10^9 N*m^2/C^2 is the proportionality factor that makes the SI units consistent. It equals 1 / (4 * pi * epsilon_0), where epsilon_0 is the permittivity of free space (8.854 x 10^-12 F/m). You do not need to look it up separately - it is built into this calculator.
How does doubling the distance affect the force?
Because force is inversely proportional to r^2, doubling the distance reduces the force to 1/4 of its original value. Tripling the distance gives 1/9 the original force. Halving the distance multiplies the force by 4. This inverse-square relationship is shared with gravity (Newton's Law of Gravitation) and the intensity of light.
Does Coulomb's Law work for charges in water or another medium?
In vacuum or air, use the formula as given. In another dielectric medium, the effective force is F / epsilon_r, where epsilon_r is the relative permittivity (dielectric constant) of the medium. For water, epsilon_r is approximately 80, so the electrostatic force between two charges immersed in water is about 80 times weaker than in vacuum.
What charge units should I use for typical physics problems?
The elementary charge on one electron or proton is about 1.6 x 10^-19 C, so picocoulombs (pC, 10^-12 C) and nanocoulombs (nC, 10^-9 C) are most convenient for atomic and molecular calculations. Lab-scale objects charged by Van de Graaff generators typically carry nanocoulombs to microcoulombs. The coulomb itself is enormous - a lightning bolt transfers only about 1 to 5 C.
How is Coulomb's Law related to Newton's Law of Gravitation?
Both laws describe forces that act at a distance and follow an inverse-square relationship (F is proportional to 1/r^2). Gravitational force is always attractive and depends on mass; electrostatic force can be attractive or repulsive and depends on electric charge. Electrostatic forces are enormously stronger: the electric force between a proton and an electron is about 10^39 times stronger than their gravitational attraction.