# Electric Field Calculator (E = kQ/r²)

Calculate electric field strength from a point charge using E = kQ/r². Also computes electric potential and force on a test charge.

## What this calculates

The electric field describes the force a charge exerts on other charges in its vicinity. For a point charge, the electric field strength at distance r is E = kQ/r², where k = 8.988 × 10⁹ N·m²/C² is Coulomb's constant. This calculator also computes the electric potential and the force that would act on a test charge placed at that point.

## Inputs

- **Charge (Q)** (C) — Typical charges are very small, e.g., 1e-6 C = 1 μC
- **Distance from Charge (r)** (m) — min 0
- **Test Charge (optional)** (C)

## Outputs

- **Electric Field Strength** (N/C) — E = kQ/r²
- **Electric Field (scientific)** (N/C) — formatted as text — Electric field in scientific notation
- **Force on Test Charge** (N) — F = qE
- **Electric Potential** (V) — V = kQ/r

## Frequently Asked Questions

**Q: What is an electric field?**

A: An electric field is a region around a charged object where other charges experience a force. The field points away from positive charges and toward negative charges. Its strength at any point tells you the force per unit charge that a small positive test charge would experience there: E = F/q.

**Q: What is Coulomb's constant?**

A: Coulomb's constant k = 8.9875 × 10⁹ N·m²/C² (often approximated as 9 × 10⁹) determines the strength of electrostatic interactions. It is related to the permittivity of free space by k = 1/(4πε₀). This constant appears in Coulomb's law and electric field equations for point charges.

**Q: How does the electric field relate to electric potential?**

A: The electric potential V = kQ/r is the potential energy per unit charge. The electric field is the negative gradient of the potential: E = -dV/dr. For a point charge, E = kQ/r² while V = kQ/r. The field tells you about forces, while potential tells you about energy.

**Q: Why does the electric field follow an inverse-square law?**

A: The electric field decreases as 1/r² because the field lines spread out over the surface of a sphere. As distance doubles, the same number of field lines passes through four times the area (since sphere area = 4πr²), so the field strength drops to one quarter. This is the same geometric reason gravity follows an inverse-square law.

---

Source: https://vastcalc.com/calculators/physics/electric-field
Category: Physics
Last updated: 2026-04-21