This calculator finds the electric field at a point. You can compute the field from a point charge or from a measured force on a test charge.

Key formulas

From a single point charge

Use Coulomb's law form:

E = k × |Q| / r²

Where:

  • E is the electric field in newtons per coulomb (N/C)
  • k is the Coulomb constant, ≈ 8.99 × 10⁹ N·m²/C²
  • Q is the source charge in coulombs (C)
  • r is the distance from the charge to the point in metres (m)

From force on a test charge

If a known force F acts on a small test charge q, use:

E = F ÷ q

Direction

The field points away from a positive charge. It points toward a negative charge. For vector problems, use unit vectors and include sign.

Examples

Example 1 — point charge

Source charge Q = 5×10⁻⁶ C. Distance r = 0.20 m.

Compute: E = 8.99×10⁹ × 5×10⁻⁶ / (0.20)²

Work: 8.99×10⁹ × 5×10⁻⁶ = 44,950. Then divide by 0.04 to get 1.12×10⁶ N/C.

Example 2 — from force

Measured force on test charge q = 1×10⁻⁶ C is F = 2×10⁻³ N.

Then E = F ÷ q = 2×10⁻³ ÷ 1×10⁻⁶ = 2000 N/C.

Example 3 — sign and direction

If Q is negative, the numeric magnitude from E = k|Q|/r² is positive, but the vector points toward the charge.

Multiple charges and superposition

For many point charges, compute the vector field from each charge. Then add the vector contributions to get the net field at the point. Do not add magnitudes unless all vectors line up the same way.

Units and valid inputs

  • Charge in coulombs (C).
  • Distance in metres (m). Keep r > 0.
  • Force in newtons (N). Test charge in coulombs (C) for the force method.

Common mistakes

  • Using mass instead of charge. Mass is not charge.
  • Forgetting the vector direction. The sign matters.
  • Using r = 0. That is not allowed for a point charge.
  • Mixing units. Convert before calculating.

When to use which formula

Use E = kQ/r² when you know the source charge and distance. Use E = F/q when you measure force on a test charge.

FAQ

What is the electric field?

It is the force per unit charge at a point in space. Units are N/C or V/m.

Why use the Coulomb constant k?

k = 8.99×10⁹ N·m²/C². It appears when using SI units for point charges.

What is a test charge?

A test charge is a small charge used to measure the field. It should not disturb the source charges.

Can I use this for continuous charge distributions?

Yes, but you must integrate the charge distribution. This page covers point charges and simple cases.

How do I add fields from many charges?

Compute each field vector and add them component-wise. This is the superposition principle.

What if I get a negative value?

A negative vector component means the field points in the negative direction of that axis. Use magnitude if you only need size.

What is the field inside a conductor?

In electrostatic equilibrium, the electric field inside a conductor is zero.

Does the field depend on test charge?

No. The field is a property of the source charges. It does not depend on the size of the test charge.

What happens near multiple charges of opposite sign?

The fields can cancel in some regions. Solve with vector addition to find where the net field is zero.

How close can I place the point to a source charge?

For a true point charge, r cannot be zero. In practice, avoid distances comparable to the size of a real charged object.

Can I use this for gravitational fields?

The form is similar, but use the gravitational constant and mass instead of charge and Coulomb constant.

What about units like microcoulomb?

Use SI prefixes. For example, 1 μC = 1×10⁻⁶ C. Convert before inserting into formulas.

How precise is Coulomb's constant?

The value 8.99×10⁹ is accurate for most classroom and engineering calculations. Use more digits for high-precision work.

Can I calculate the field of a ring or disk here?

Not directly. Those require integral formulas. This page focuses on point charges and vector addition.

How to handle vector components?

Find the radial unit vector from source to point. Multiply magnitude by that unit vector. Then sum components for multiple charges.

Is electric field same as electric potential?

No. The electric field is a vector. Potential is a scalar. E is the negative gradient of potential.