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Electric Field Calculator

Calculate point-charge field strength, direction, and test-charge force.

Electric Field Calculator tool

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About This Tool

An electric field describes the force that a positive test charge would experience per unit charge at a location. For an isolated point charge in vacuum, its magnitude depends on the source charge and the inverse square of the distance. This calculator applies E = k|q|/r², reports the radial direction implied by the source charge, and uses F = qE to find the magnitude and relative direction of force on a signed test charge. All calculations run locally in your browser.

How To Use It

  1. Enter the source charge. Use a positive value for a positive charge or a negative value for a negative charge.
  2. Choose the charge unit and enter a distance greater than zero from the point charge.
  3. Select the electric-field result unit. N/C and V/m represent the same electric-field dimension.
  4. Interpret the direction as radial: away from a positive point charge and toward a negative point charge.
  5. Enter a signed test charge to calculate force. Positive charges feel force along the electric field; negative charges feel force in the opposite direction.
  6. Review the SI conversions and substituted formulas beneath the results to verify how the field and force were calculated.

Examples

1 µC at 0.1 m

A +1 µC point charge at 0.1 m produces an ideal field magnitude of about 8.99 × 10^5 N/C, directed away from the positive charge.

Negative source charge

Changing the source charge from positive to negative leaves the magnitude unchanged for the same |q| and distance, but reverses the radial direction toward the charge.

Inverse-square behavior

Doubling the distance from the same point charge reduces the field magnitude to one quarter because E is proportional to 1/r².

Force on a negative test charge

A 2,000 N/C field acting on a −3 µC test charge produces 0.006 N of force opposite the electric-field direction. The magnitude uses |q|E while the sign determines direction.

Useful Notes

Point-charge electric field formula

For a point charge in vacuum, E = k|q|/r², where E is electric-field magnitude, q is source charge, r is distance from the charge, and k is Coulomb's constant, approximately 8.9875517923 × 10^9 N·m²/C².

Direction and charge sign

Electric-field direction is defined as the direction a positive test charge would accelerate. The field points radially away from a positive source charge and radially toward a negative source charge. A zero source charge produces zero field, so there is no meaningful radial field direction.

N/C and V/m

Newtons per coulomb and volts per metre are equivalent SI expressions for electric-field strength. This calculator offers both forms plus kilo-scaled versions for convenient reading.

Why distance matters so much

The inverse-square relationship means field strength falls rapidly with distance. If distance is multiplied by three, the ideal field becomes one ninth as large; if distance is halved, the field becomes four times as large.

Force on a test charge

Electric field is force per unit positive charge, so a test charge q experiences force magnitude |F| = |q|E. A positive test charge is pushed along the field direction and a negative test charge is pushed opposite it. The test charge is assumed small enough that it does not disturb the source configuration.

Calculation steps and unit conversion

The result first converts source charge, test charge, and distance to coulombs and metres. It then substitutes those SI values into E = k|q|/r² and |F| = |qₜ|E so the displayed magnitudes can be checked independently. Charge signs are retained in the conversion steps because they determine field and force direction, even though magnitudes use absolute values.

Model assumptions and limitations

The formula models a single ideal point charge in vacuum. Extended charge distributions, multiple charges, conductors, dielectric materials, boundaries, and time-varying electromagnetic effects require additional methods. At r = 0 the ideal point-charge expression is singular, so the calculator requires a positive distance.

FAQ

What is the formula for electric field from a point charge?

The magnitude is E = k|q|/r² for an isolated point charge in vacuum. The sign of q determines the radial direction rather than making the magnitude negative.

Why does the calculator use absolute charge for magnitude?

Magnitude is non-negative. A negative source charge changes the field direction toward the charge, while a positive source charge makes the field point away.

Are N/C and V/m the same?

Yes. For electric field, 1 N/C is equivalent to 1 V/m.

Can I calculate the net field from several charges?

Not with this single-point-charge calculator. Electric fields from multiple sources must be added as vectors, including their directions and geometry.

How do I find force from electric field?

Multiply field magnitude by the absolute test-charge value: |F| = |q|E. Use the charge sign for direction: positive along the field, negative opposite the field.