Electric Field Calculator
Solve E = F/q for the electric field from force and charge, or E = kQ/r² for the field created by a point charge at a distance. Two 3D diagrams show field-line density near and far from a point charge, and charts show how field strength falls off with distance and scales with charge.
Reviewed by the ToolNestr Editorial Team — July 2026
Field-line density near and far from a charge
1. Close to the charge — strong field
Field-line arrows sampled at a near distance from a positive point charge, radiating outward densely — a strong field.
2. Far from the charge — weak field
The same charge sampled at a farther distance — arrows are sparser and shorter, showing the field has weakened with the inverse-square drop-off.
Electric field graphs
How it works
The core idea in one line: An electric field describes the force per unit charge that would act on a small test charge at every point around a charged object — it exists whether or not a test charge is actually there to feel it.
E = F / q
electric field from force on a test charge
E = k Q / r²
field of a point charge; k ≈ 8.9875×10⁹ N·m²/C²
From E = F/q, force and charge solve directly: F = qE and q = F/E. For the field of a point charge, E = kQ/r² rearranges to Q = Er²/k and r = √(kQ/E). Because E falls off as 1/r², doubling the distance from a point charge cuts the field to a quarter — the same inverse-square drop-off as Coulomb's law itself, since the field is just force divided by a test charge.
Worked example 1 — field from a point charge
Given: A point charge Q = 2 μC (2×10⁻⁶ C) sits at the origin. Find the electric field at r = 0.5 m.
Halving the distance to 0.25 m would quadruple this field to 287,600 N/C, since E falls off as 1/r².
Worked example 2 — force from field and charge
Given: A uniform electric field of E = 500 N/C acts on a charge q = 4 μC (4×10⁻⁶ C). Find the force on the charge.
The force direction matches the field direction for a positive charge, and points opposite the field for a negative charge.
Electric field vs gravitational field
Both are "force per unit source quantity" fields with an inverse-square dependence on distance from a point source.
| Property | Electric field | Gravitational field |
|---|---|---|
| Formula (point source) | E = kQ/r² | g = GM/r² |
| Source quantity | Charge Q | Mass M |
| Force on a test object | F = qE | F = mg |
| Can point either way | Yes — away from + charge, toward − charge | No — always toward the mass |
Both fields obey an inverse-square law, but the electric field can point toward or away from its source depending on charge sign, while gravity is always attractive.
Where electric fields actually matter
🖨️ Laser printers and photocopiers
A charged drum creates an electric field that attracts oppositely charged toner particles to exactly the right spots on the page, using the same E = F/q relationship that governs any charged particle in a field.
🌩️ Thunderstorm electric fields
Charge separation inside storm clouds builds up an electric field strong enough — often tens of thousands of volts per metre — to ionise air and trigger a lightning strike once it exceeds air's dielectric breakdown strength.
🧪 Mass spectrometers and particle accelerators
Charged particles are steered and accelerated using carefully shaped electric fields, where the force F = qE determines exactly how much a particle of known charge will bend or speed up.
📺 Old CRT televisions
Cathode ray tubes used electric fields between charged plates to deflect a beam of electrons left, right, up, and down thousands of times per second to paint an image on the phosphor screen.
Common misconceptions
"The electric field is the same thing as the force."
Field and force are related but distinct: E = F/q means the field is force per unit charge. The same field E produces different forces on different charges — a bigger charge in the same field feels a bigger force, F = qE.
"A stronger field always means a bigger charge is present."
Field strength from a point charge, E = kQ/r², depends on both the charge and the distance. A modest charge very close by can create a stronger field than a huge charge far away — distance matters just as much as charge magnitude.
"Electric field lines are physically real, like wires."
Field lines are a visualization tool showing the direction a test charge would be pushed or pulled at each point — there is nothing physically there. Line density is just a convenient way to represent field strength, with denser lines meaning a stronger field.
"The field only exists where there is a test charge to feel it."
The electric field exists at every point in space around a charge, whether or not another charge is there to experience it — placing a test charge just reveals the field that was already present, it does not create it.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 2 — §5.4 "Electric Field" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 22, Electric Fields.
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 23, Electric Fields.
E = F/q and E = kQ/r² with k ≈ 8.9875×10⁹ N·m²/C². Results are rounded for display.
How to use this calculator
Pick a mode
Use "From force and charge" for E = F/q, or "From point charge" for E = kQ/r².
Enter charges in coulombs
Use scientific notation for lab-scale charges, e.g. 2e-6 for 2 μC.
See the field visually
The 3D diagrams show field-line density falling off with distance from the source charge.
Related tools
Frequently asked questions
What is an electric field?
An electric field is the region around a charged object where another charge would feel a force. Its strength E at a point is defined as the force per unit charge a small positive test charge would feel there: E = F/q, measured in newtons per coulomb (N/C).
What is the formula for the field of a point charge?
E = kQ/r², where k ≈ 8.9875×10⁹ N·m²/C² is Coulomb's constant, Q is the source charge, and r is the distance from it. This is the same inverse-square shape as Coulomb's law itself, since F = qE = kQq/r².
How is the electric field related to Coulomb's law?
Coulomb's law gives the force between two charges, F = kq₁q₂/r². The electric field is what one charge creates at every point in space; multiplying that field by a second charge's magnitude gives the force on it, F = qE — so E = kQ/r² is just Coulomb's law divided by the test charge.
Does the electric field depend on the test charge placed in it?
No — the field E = kQ/r² is a property of the source charge Q and the distance r alone. A test charge only experiences the field; it does not change it (assuming the test charge is small enough not to disturb the source charge's position).
Which way does the electric field point?
By convention, field lines point away from positive charges and toward negative charges — showing the direction the force on a small positive test charge would point at that location.