Electric Field Calculator
Find the electric field strength three ways: from a point charge with E = k·q ÷ r², between parallel plates with E = V ÷ d, or from the force on a test charge with E = F ÷ q. Switch the charge, distance and field units, set the surrounding medium, and read the force a test charge would feel.
Formula
Worked example
A 1 nC charge 10 cm away in air: E = (8.99×10⁹ × 1×10⁻⁹) ÷ (1 × 0.1²) = 8.99 ÷ 0.01 ≈ 899 N/C, pointing away from the charge. Place a 1 nC test charge there and it feels F = 1×10⁻⁹ × 899 ≈ 9 × 10⁻⁷ N.
Three ways to find the electric field
The electric field describes the force a unit positive test charge would feel at a point in space, and this calculator finds it three ways. For a single point charge the field magnitude is Coulomb’s constant k times the charge q divided by the square of the distance r, and divided by the relative permittivity of the surrounding medium: E = k·q ÷ (εᵣ·r²). Between two parallel plates the field is uniform and equals the voltage divided by the gap, E = V ÷ d. And whenever you can measure the force on a known test charge, the field is simply that force divided by the charge, E = F ÷ q. All three give the same quantity in newtons per coulomb (N/C), which is identical to volts per metre (V/m).
The medium, the sign, and the inverse-square law
For a point charge the r² in the denominator means the field weakens rapidly with distance: move twice as far and the field drops to one-quarter; move ten times as far and it drops to one-hundredth. The relative permittivity εᵣ accounts for the material around the charge: vacuum and air are about 1, glass is roughly 5, and water is about 80, so the same charge in water produces a field about 80 times weaker. The field points radially outward from a positive charge and inward toward a negative one, which is why the sign of q carries the direction. Once the field exceeds roughly 3 × 10⁶ N/C the air begins to ionise and break down, the threshold behind sparks and lightning.
From field to force on a test charge
The electric field is most useful because it tells you the force on any charge placed in it. Turn on the test-charge option and the calculator multiplies the field by the probe charge to give F = q·E in newtons. A positive test charge is pushed along the field direction, a negative one against it. This is the bridge between the field and Coulomb’s law: the field is the force per unit charge, so once you know E at a point, the force on a real charge there is immediate. The same relationship underlies how capacitors, particle accelerators and electrostatic precipitators all put electric fields to work.
Electric field in familiar situations
| Scenario | Setup | Field (N/C) |
|---|---|---|
| 1 nC at 1 cm in air | E = kq/r² | 8.99 × 10⁴ |
| 1 nC at 10 cm in air | E = kq/r² | 899 |
| 1 nC at 10 cm in water | εᵣ ≈ 80 | ≈ 11 |
| 12 V across a 2 mm gap | E = V/d | 6 000 |
| Air breakdown threshold | sparks begin | ≈ 3 × 10⁶ |
How the same field idea spans many orders of magnitude across charge, distance, voltage and medium.
Frequently asked questions
What is the formula for the electric field of a point charge?
The electric field of a point charge is E = k·q ÷ (εᵣ·r²), where k is Coulomb’s constant 8.99 × 10⁹ N·m²/C², q is the source charge, r is the distance from the charge, and εᵣ is the relative permittivity of the surrounding medium (1 for vacuum or air). The result is the field strength in newtons per coulomb (N/C), equal to volts per metre.
How do I find the field between two parallel plates?
Between parallel plates the field is uniform and equals the voltage divided by the plate separation: E = V ÷ d. Switch this calculator to the parallel-plate mode, enter the voltage and the gap, and it returns the field in N/C or V/m. A smaller gap at the same voltage gives a stronger field, which is why thin-gap capacitors hold large fields.
How does the medium change the electric field?
The relative permittivity εᵣ of the material around a charge divides the field strength. Vacuum and air are about 1, so they barely change it, but glass is roughly 5 and water about 80. The same point charge in water therefore produces a field roughly 80 times weaker than in air, because the medium partly screens the charge.
What does a negative field result mean?
In point-charge mode a negative source charge gives a negative field value, signalling that the field points radially inward, toward the charge, rather than outward. The magnitude, the size of the number, is the actual field strength regardless of sign. Multiply the field by a test charge to get the force, F = q·E.
What are the units of the electric field?
Electric field is measured in newtons per coulomb (N/C), which is exactly equivalent to volts per metre (V/m). Both describe the force per unit charge the field exerts, or equivalently how steeply the electric potential changes over distance. This calculator reports both forms.