Electric Field Calculator

What the electric field calculator does

A point charge creates an electric field around it, and this calculator finds the strength of that field at a chosen distance. It works from the charge and the distance, with an option for the surrounding material, and can combine the contributions of several charges.

Below is what an electric field is, the equation behind it, why it falls off with the square of distance, and a worked example.

How to use it

1. Choose a single point charge or a system of point charges.
2. Enter the charge and the distance, using advanced mode to set the relative permittivity if needed.
3. Press Calculate for the electric field strength, or Reset to clear it.

What an electric field is

An electric field is the region of influence that surrounds an electric charge, the means by which one charge pushes or pulls on another without touching it. Any charge creates a field in the space around it, and any other charge placed in that field feels a force. The electric field at a point tells you how strong that influence is there, defined as the force that would act on a unit of positive charge placed at that point. It is measured in newtons per coulomb, force per unit charge.

The field is a way of describing how the effect of a charge reaches out across space and weakens with distance. Close to the charge the field is strong, and far away it is weak, fading but never quite vanishing. The field is a vector, having a direction as well as a strength, pointing away from positive charges and toward negative ones. The electric field is one of the most fundamental concepts in physics, underlying all electrical and electronic phenomena. This calculator computes its strength for the field of a point charge, the simplest and most basic case.

The equation it uses

The electric field of a single point charge is given by Coulomb's law in field form:

E = k × Q ÷ r²

Here E is the field strength, Q is the charge, r is the distance from the charge, and k is Coulomb's constant, which sets the scale of electrical forces. The field is proportional to the charge, so a larger charge makes a stronger field, and it is inversely proportional to the square of the distance, so it weakens rapidly as you move away. In a material rather than empty space, the field is reduced by the material's relative permittivity, which the calculator allows you to include. It evaluates this relationship from the charge and distance you provide.

The inverse-square falloff

The most important feature of a point charge's field is that it falls off with the square of the distance, an inverse-square law. Double the distance from the charge and the field drops to a quarter, not a half; triple the distance and it drops to a ninth. This rapid weakening with distance is the same mathematical pattern seen in gravity and in the spreading of light, and it arises because the influence of the charge spreads out over the surface of an ever-larger sphere as you move away.

This inverse-square behaviour means the field is intensely strong very close to a charge and fades quickly with distance, which has far-reaching consequences. It explains why electrical forces are dominant at the atomic scale, where distances are tiny, yet are easily shielded and rarely felt over large distances in everyday life. Understanding the steep falloff is key to predicting how charges interact and how fields behave around them. The calculator makes the falloff concrete, showing how dramatically the field strength changes as the distance to the charge varies.

Direction and combining fields

Because the electric field is a vector, it has direction as well as magnitude, and this matters when more than one charge is present. The field from a single point charge points directly away from it if the charge is positive, or directly toward it if negative, along the line connecting the charge to the point in question. The strength this calculator gives is the magnitude of that field, with the direction set by the sign of the charge.

When several charges are present, their fields combine by the principle of superposition: the total field at any point is the vector sum of the fields from all the individual charges, each added with its own strength and direction. This is how the field of any arrangement of charges is found, by adding up the contributions one charge at a time. The vector nature means fields can reinforce or partly cancel depending on the directions involved, which is why the geometry of a charge arrangement shapes the overall field. The single-charge field this calculator computes is the basic ingredient from which these combined fields are built.

Units and precision

The calculator takes the charge in coulombs and its smaller multiples, or in elementary charges, and the distance in a range of units from nanometres upward, returning the electric field strength in newtons per coulomb. It uses the standard value of Coulomb's constant and lets you set the relative permittivity of the surrounding medium in advanced mode, with empty space or air as the default. The point-charge relationship is exact for an ideal point charge, the standard idealisation for this kind of calculation.

A worked example

Suppose a charge of 1 microcoulomb sits in air, and you want the field strength 1 metre away.

The field is E = k × Q ÷ r² = (8.99 × 10&sup9;) × (0.000001) ÷ 1² ≈ 8,990 newtons per coulomb. Move out to 2 metres and the field drops to about 2,250 newtons per coulomb, a quarter of the value, because doubling the distance quarters the field through the inverse-square law.

Questions people ask

How do you calculate the electric field of a point charge?

Use E = k × Q ÷ r², from the charge, the distance, and Coulomb's constant. The field grows with charge and falls with the square of distance.

Why does the field fall off with distance squared?

Because the charge's influence spreads over the surface of an expanding sphere, whose area grows with the square of the radius. So the field weakens as one over distance squared.

Which way does the field point?

Away from a positive charge and toward a negative one, along the line joining the charge to the point. The field is a vector with both strength and direction.

How do fields from several charges combine?

By vector addition, the principle of superposition. The total field is the sum of the individual fields, accounting for both their strengths and directions.

References

A quick note on where the physics comes from. The electric field of a point charge, Coulomb's law, and superposition are standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. Coulomb's constant follows NIST. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 5.5, Electric Field. https://openstax.org/books/university-physics-volume-2/pages/5-5-electric-field
2. HyperPhysics, Electric Field of Point Charge. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html
3. National Institute of Standards and Technology (NIST), Fundamental Physical Constants, Coulomb constant. https://physics.nist.gov/cuu/Constants/