About the Electric Field Calculator
This electric field calculator finds the strength of an electric field in three common situations. Around a point charge it uses Coulomb’s law to give the field E = kq/r² and the electric potential V = kq/r at any distance. Between two parallel plates it gives the uniform field E = V/d from the voltage and the gap. And if you know the force on a small test charge, it returns the field as E = F/q.
It is aimed at physics students working through electrostatics homework, teachers preparing examples, and hobbyists who want a feel for the fields inside capacitors or around charged objects. In every mode you can enter a test charge to see the force the field would exert on it, and the point-charge mode draws a chart of how quickly the field fades with distance.
The point-charge formula assumes a point (or a uniformly charged sphere measured from its centre) in a uniform medium; enter a relative permittivity above 1 for a material such as water or oil. The parallel-plate result assumes the plates are large compared with the gap, so edge effects are negligible. Field strength is reported in newtons per coulomb, which is identical to volts per metre.
How to use the electric field calculator
- 1Choose the situation: a point charge, parallel plates, or a measured force on a test charge.
- 2Enter the charge and distance, the plate voltage and gap, or the force.
- 3Pick the charge and distance units.
- 4Optionally enter a test charge to see the force the field exerts on it.
- 5Read the field strength, direction and (for a point charge) the electric potential.
Formula and method
The electric field at a point is the force per unit charge that a small positive test charge would feel there. For a single point charge it follows from Coulomb’s law: the field strength falls with the square of the distance, while the potential (energy per unit charge) falls only with the distance itself, and carries the sign of the charge. Coulomb’s constant k = 1/(4πε₀) ≈ 8.98755 × 10⁹ N·m²/C² uses the CODATA 2022 vacuum permittivity; a dielectric medium divides both E and V by its relative permittivity εr.
Between two large, closely spaced parallel plates the field is uniform and equals the potential difference divided by the gap, which is why field strength can be quoted in volts per metre — the same unit as newtons per coulomb. If you measure the force on a known test charge instead, the field is simply E = F/q₀. In all modes the force on a test charge is F = q₀E.
- E
- Electric field strength (N/C = V/m)
- V
- Electric potential (V), or plate voltage in E = V/d
- q
- Source charge (C)
- q₀
- Test charge (C)
- r
- Distance from the point charge (m)
- d
- Plate separation (m)
- k
- Coulomb constant, 8.98755 × 10⁹ N·m²/C²
- εr
- Relative permittivity of the medium
Worked examples
5 nC charge, 10 cm away
E = 8.98755 × 10⁹ × 5 × 10⁻⁹ / 0.1² = 4,494 N/C and V = 8.98755 × 10⁹ × 5 × 10⁻⁹ / 0.1 = 449.4 V. A 1 nC test charge placed there feels 1 × 10⁻⁹ × 4,494 = 4.49 µN, pushed away from the positive source charge.
12 V across plates 2 mm apart
The uniform field is E = 12 V / 0.002 m = 6,000 V/m (N/C). A 2 nC test charge between the plates feels 2 × 10⁻⁹ × 6,000 = 1.2 × 10⁻⁵ N, i.e. 12 µN.
Field from a measured force
A 2 µC test charge feels 0.003 N, so the field is E = 0.003 / (2 × 10⁻⁶) = 1,500 N/C.
Proton’s field at the Bohr radius
One elementary charge (1.602 × 10⁻¹⁹ C) at 0.0529 nm gives E = k e / r² ≈ 5.15 × 10¹¹ N/C and a potential of about 27.2 V — the scale of the electric forces that hold the hydrogen atom together.
Frequently asked questions
What is the formula for the electric field of a point charge?+
E = kq/r², where k ≈ 8.99 × 10⁹ N·m²/C², q is the charge in coulombs and r the distance in metres. The field points away from a positive charge and toward a negative one.
What is the difference between electric field and electric potential?+
The field (N/C or V/m) is the force per unit charge and is a vector. The potential (volts) is the potential energy per unit charge and is a scalar. Around a point charge E falls as 1/r² while V falls as 1/r.
Are N/C and V/m the same unit?+
Yes. One newton per coulomb equals one volt per metre, because a volt is a joule per coulomb and a joule is a newton-metre. Both describe electric field strength.
How do you calculate the field between parallel plates?+
Divide the voltage by the separation: E = V/d. For 12 V across 2 mm the field is 6,000 V/m. This holds when the plates are much wider than the gap, so the field between them is uniform.
How strong an electric field causes a spark in air?+
Dry air at sea level breaks down at roughly 3 million volts per metre (3 kV/mm). Humidity, sharp points and lower pressure all reduce the voltage needed for a spark.
How do I find the force on a charge in an electric field?+
Multiply the charge by the field: F = qE. A positive charge is pushed along the field direction and a negative charge (like an electron) is pushed the opposite way.