Calculating Electric Field: Formula and Examples

Calculate electric field by dividing the force on a small positive test charge by the charge: E = F/q. For a point source charge, use E = k|Q|/r²; enter the source charge and distance to get the field magnitude, with direction determined by the source’s sign and position.

Formula

For a point charge in vacuum, the electric field magnitude is E = k|Q|/r². Here, E is electric-field magnitude in newtons per coulomb (N/C), Q is the source charge in coulombs (C), r is the separation from the charge in metres (m), and k is Coulomb’s constant, approximately 8.9875517923 × 10⁹ N·m²/C². The calculator accepts Q in microcoulombs (μC), so it converts that value to coulombs by multiplying by 0.000001. One N/C is numerically equal to one volt per metre (V/m).

The first output is the field magnitude, not a signed direction. For a positive source charge, the field points away from it; for a negative source charge, it points toward it. The separate V/m output is the same magnitude in an equivalent unit.

Worked Example

Using the calculator’s default values, Q = 1 μC = 0.000001 C and r = 0.1 m:

1. Square the distance: r² = (0.1 m)² = 0.01 m².
2. Calculate E = (8.9875517923 × 10⁹)(0.000001) / 0.01.
3. E = 898755.17923 N/C, which rounds to 898755.18 N/C.
4. In equivalent units, the field is 898755.18 V/m.

This result is the magnitude at a point 0.1 m from an isolated positive 1 μC charge in vacuum. Its direction is radially outward from the charge.

What Electric Field Means

Electric field describes how a charged object influences the space around it. At any location, the field gives the force that would act on each unit of positive charge placed there. Its vector definition is E = F/q, where F is the electric force in newtons and q is the test charge in coulombs. If the test charge is negative, the force is opposite the field direction; the field itself is defined using the force direction on a positive test charge.

Electric field is a vector, so it has both magnitude and direction. A calculator using absolute charge and distance supplies only the magnitude. To fully describe the field, also state where it points, or give its components along chosen axes.

Choosing the Right Calculation

The point-charge formula is appropriate when the source can be treated as a point, or when evaluating the field outside a spherically symmetric charge distribution. It is also a good approximation when the distance is much larger than the physical size of the charged object. The calculator assumes vacuum; for many introductory calculations, air is approximated as vacuum.

Use the force definition when the force on a known test charge is given. Rearranging it gives E = F/q. For example, if a 2 μC test charge experiences a 0.006 N force, the field magnitude is 0.006/(2 × 10⁻⁶) = 3000 N/C. This method requires force and test charge to refer to the same location and setup.

For several point charges, calculate each field as a vector and add the vectors. Do not simply add magnitudes unless all contributions point in the same direction. A continuous line, sheet, or volume of charge generally requires an integration or a symmetry-based result rather than treating the whole object as one point charge.

Units, Direction, and Common Mistakes

• Convert charge before using the formula. One microcoulomb is 10⁻⁶ C; one nanocoulomb is 10⁻⁹ C. Entering a number in μC as though it were C makes the result one million times too large.
• Use distance, not its square, as the input. The formula squares r. Doubling distance reduces the field to one quarter; doubling source-charge magnitude doubles the field.
• Keep units consistent. This calculator uses metres and produces N/C or V/m. If given centimetres, divide by 100 to obtain metres. In US customary units, convert feet to metres before using this version: 1 ft = 0.3048 m. The SI result can then be converted if another unit is required.
• Separate magnitude from direction. Absolute value in the calculation makes the output positive. The sign of Q determines whether field lines point outward or inward.
• Round only at the end. The displayed value is rounded to two decimal places; intermediate rounding can cause small differences.

Limits and Physical Interpretation

The field grows rapidly near a point charge according to the inverse-square law. At r = 0, the point-charge expression is undefined; an ideal point charge has a mathematical singularity there. Do not interpret the formula as a realistic description of the internal field of an extended charged object. For an extended source, its size and charge distribution matter.

In a material medium, the field for a given free charge can differ from the vacuum result because the material responds to the field. A simple substitution involving permittivity can apply in specified idealized situations, but real materials and boundaries may require a more complete electrostatic model. The calculator does not include those effects, nearby charges, or time-varying electromagnetic fields.

A common misconception is that electric field is the same thing as electric force. It is not: field is force per unit charge, while the force on a particular charge is F = qE. Another useful distinction is between electric field and electric potential. Potential is a scalar measured in volts; field is a vector measured in N/C or V/m. In a uniform field, the potential change along the field direction is related to distance by ΔV = −Ed, but that simple relation does not apply unchanged to every geometry.

Frequently Asked Questions

What is the formula for electric field?
For a point charge, the magnitude is E = k|Q|/r². More generally, electric field is force per unit positive test charge, E = F/q.

What unit is electric field measured in?
Common SI units are newtons per coulomb (N/C) and volts per metre (V/m). They are equivalent in magnitude: 1 N/C = 1 V/m.

Does a negative charge make the electric field negative?
The field’s magnitude is not negative. A negative source charge makes the field point toward the source; a positive source charge makes it point away. A signed component can be negative if it points opposite the chosen coordinate direction.

How does distance affect electric field?
For a point charge, field magnitude varies as 1/r². If the distance doubles, the field becomes one quarter as strong; if it triples, it becomes one ninth as strong.

How do you calculate the field from multiple charges?
Find each charge’s field at the location of interest, resolve each into vector components, and add corresponding components. The result depends on both the charges and their positions.

Can I use this formula inside a charged sphere?
Not generally by treating the sphere’s total charge as a point at its centre. The internal field depends on how charge is distributed. A uniformly charged solid sphere, a conducting sphere, and other distributions have different interior fields.

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in q | Source charge | μC | 1 | 0
in r | Distance | m | 0.1 | 0
out E | Electric field magnitude | N/C | 8987551792.3 * abs(q) * 0.000001 / (r ^ 2) | 2
out Vpm | Electric field | V/m | E | 2