Coulomb's Law Force Calculator

Physics Electricity and Magnetism • Electric Fields and Charges

Written by STEM Calculators Team Published January 10, 2026 Updated February 24, 2026

1. Coulomb’s Law Force Calculator

Compute electrostatic force between point charges using Coulomb’s law: $\mathbf{F}=k\,q_i q_j\,\dfrac{\mathbf{r}_i-\mathbf{r}_j}{\|\mathbf{r}_i-\mathbf{r}_j\|^3}$ (vector) and $F=k\,\dfrac{|q_1 q_2|}{r^2}$ (magnitude). Supports a multi-charge net-force mode and dielectric media via $k=\dfrac{1}{4\pi\varepsilon_0 \varepsilon_r}$ .

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication. Scientific notation like 2e-6 is supported.

Mode + Inputs

Mode: Constant: Coulomb constant $k$ (N·m²/C²): $\varepsilon_0$ (F/m): $\varepsilon_r$ (relative permittivity): Compute force on: Charge 1 $q_1$ (C): Position 1 $x_1$ (m): Position 1 $y_1$ (m): Charge 2 $q_2$ (C): Position 2 $x_2$ (m): Position 2 $y_2$ (m): Charges list (multi): Target index (1-based): Parsed charges:

Force vector plot: Arrow animation $\tau\in[0,1]$: Play speed:

Two-charge mode: choose “force on charge 1 or 2”. Multi mode: paste one charge per line as q, x, y, then click Solve.

Ready

Steps

Enter values and click Solve.

Force vector plot

Charges + net force arrow (pan/zoom)

Hover: (x, y)=…

Scroll to zoom. Drag to pan. Double-click to reset. Colors: red = $+$, blue = $-$. The ring is the target; the arrow is the force on the target.

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Theory: Coulomb’s Law and Force Vectors

Coulomb’s law describes the electrostatic force between point charges. The force acts along the line joining the charges, and its direction depends on whether the charges are like (repel) or unlike (attract).

1) Magnitude form

For two charges $q_1$ and $q_2$ separated by distance $r$, \[ F = k\,\frac{|q_1 q_2|}{r^2}, \] where $k \approx 8.99\times 10^9\,\mathrm{N\,m^2/C^2}$ in vacuum.

2) Vector form (recommended for direction)

Let positions be $\mathbf{r}_1=(x_1,y_1)$ and $\mathbf{r}_2=(x_2,y_2)$. A common vector expression for the force on charge $i$ due to charge $j$ is: \[ \mathbf{F}_i = k\,q_i q_j\,\frac{\mathbf{r}_i-\mathbf{r}_j}{\|\mathbf{r}_i-\mathbf{r}_j\|^3}. \] This automatically handles attraction vs. repulsion through the sign of $q_i q_j$.

3) Multiple charges (superposition)

Electric forces add as vectors. The net force on charge $i$ from many charges is: \[ \mathbf{F}_{net} = \sum_{j\ne i}\mathbf{F}_{i\leftarrow j}. \] This is called the principle of superposition.

4) Dielectrics and effective $k$

In a linear dielectric medium, the permittivity becomes $\varepsilon=\varepsilon_0\varepsilon_r$, so: \[ k=\frac{1}{4\pi\varepsilon_0\varepsilon_r}. \] Larger $\varepsilon_r$ reduces the force magnitude compared to vacuum.

Website tip: In the plot, red dots represent positive charges and blue dots represent negative charges. The highlighted ring is the target charge; the arrow shows the computed force direction.

Steps

Force vector plot

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