This electric potential calculator computes the voltage created by a point charge — V = kQ/r — plus the potential energy of a second charge placed in that field and the work needed to move it there. Potential is the scalar half of electrostatics: no directions, no vector components, just energy per charge — and for most circuit intuition, it’s the half that matters.

Electric potential V at r –
Potential energy U of test charge –
Field strength E at r (for scale) –

Potential is defined with zero at infinity: V is the work per unit charge to bring a test charge from infinitely far away to distance r, against (or with) the source’s field. k = 8.988×10⁹ N·m²/C².

Potential: The Landscape Picture of Electricity

If the electric field is a slope map, potential is the elevation map. V = kQ/r assigns every point in space a height — the energy a unit charge would own just by standing there. Charges roll downhill in this landscape: positive charges slide toward lower potential, electrons climb it happily, and the steepness of the slope (E = −dV/dr) is the field strength. The enormous practical advantage: potential is a scalar. Potentials from many charges simply add as numbers, V = Σ kQᵢ/rᵢ, with no components to resolve — the standard trick for multi-charge problems, and the reason circuit theory can be built on voltages at nodes without ever drawing a field vector.

The definition hides a choice: V is measured relative to infinity, where it’s defined as zero. That convention makes a lone positive charge create positive potential everywhere (you must push a positive test charge in, doing positive work), and a negative charge create a negative well (the field does the work; you’d have to hold the test charge back). Every battery, power supply and “ground” in engineering is this same move — pick a reference, measure heights from it. Our Electric Field Calculator is the vector sibling: it returns E where this page returns V, and for a point charge the two obey E = V/r exactly, which the results table verifies numerically.

Worked Examples (Verified)

  • 2 µC at half a meter (defaults): V = kQ/r = 35,950 V ≈ 36.0 kV — static-electricity scale: a doorknob spark involves comparable voltages at far smaller charges and distances. The test charge of 1 µC placed there owns U = V·q = 0.0360 J of potential energy.
  • The electron-volt connection: one electron moved through 1 V gains exactly 1 eV = 1.602×10⁻¹⁹ J — the energy currency of atomic physics and the reason electron microscopes are rated in “accelerating voltage”: a 100 kV microscope gives each electron 100 keV.
  • Superposition sanity check: two opposite charges (a dipole) at equal distance from a midpoint contribute V = kq/r + k(−q)/r = 0 exactly — the midpoint is at zero potential even though the field there is strongly nonzero. Scalar addition behaving beautifully, vector addition doing the opposite, in one example.

Where Potential Runs the World Quietly

  • Van de Graaff and accelerators: terminal voltage IS the particle energy — a 3 MV terminal accelerates protons to 3 MeV. Potential isn’t a metaphor in accelerator physics; it’s the spec sheet.
  • Lightning: cloud-to-ground potentials reach hundreds of megavolts before air breaks down (~3 MV/m) — the potential builds silently until the landscape itself fails.
  • Membrane potentials: a living cell maintains about −70 mV across a 5 nm membrane — a tiny voltage across a nanometer gap, i.e. a field of ~14 million V/m, which is how biology runs enormous field strengths at harmless voltages.
  • Equipotential safety: birds sit on 100 kV lines unharmed because both feet are at the same potential — no difference, no current. Linemen bond themselves to the line’s potential for the same reason.

Potential Discipline

  • Only differences are physical: add a constant to every V and nothing observable changes (the field, −slope of V, is untouched) — the gauge freedom that makes “ground” a free choice.
  • Inside a conductor, V is constant (electrostatic equilibrium): all the slope lives outside, which is why a hollow charged shell shields its interior — the Faraday cage.
  • Point-charge formulas diverge at r → 0 — real charges have size; treat sub-millimeter distances with the formulas’ spirit, not their letter.
  • Energy bookkeeping: U for a pair is kQq/r, shared by the pair — assemble three charges and you sum over the three pairs (not six — double counting pairs is the standard bookkeeping error).

Related Tools

Frequently Asked Questions

How do you calculate electric potential?

For a point charge: V = kQ/r, with k = 8.988×10⁹ N·m²/C², Q in coulombs and r in meters. A 2 µC charge at 0.5 m gives V = 35,950 V. For several charges, add the individual potentials as signed scalars — no vector components needed, which is the practical reason potential exists as a concept. This calculator also returns the potential energy U = V·q of a test charge and the field strength at the same point.

What is the difference between electric potential and potential energy?

Potential (volts) is a property of the place — energy per unit charge, independent of what you put there. Potential energy (joules) is a property of the charge placed: U = qV. A location at 36 kV gives a 1 µC charge 0.036 J and a 2 µC charge 0.072 J, at the same potential. Confusing the two is the volts-versus-joules error that haunts first-year problem sets.

Why is potential zero at infinity?

By convention, chosen because the force between charges fades to nothing at infinite separation — the one reference point every charge configuration agrees on. It makes isolated positive charges positive-potential and negative charges negative-potential, and gives U = kQq/r its clean form. Engineers make the same choice locally when they declare a chassis or earth “ground” (0 V) and measure everything against it.

Can electric potential be negative?

Yes — a negative source charge creates negative potential everywhere around it (a well instead of a hill), and mixed configurations produce both signs with a zero-potential surface between them (for a dipole, the entire mid-plane). Negative potential simply means a positive test charge would have negative potential energy there — bound, like an electron in an atom’s potential well, which is exactly the picture atomic physics uses.

How are electric field and potential related?

The field is the negative slope of the potential: E = −dV/dr (pointing downhill in potential). For a point charge, E = kQ/r² = V/r. Closely spaced equipotential surfaces mean a strong field; wide spacing means a weak one — the same reading as contour lines on a topographic map. When a problem is hard in field form (vectors) it often collapses in potential form (scalars), then differentiates back at the end.

What does 1 volt actually mean?

One joule of work per coulomb of charge moved: a 1.5 V battery hands 1.5 J to every coulomb it pushes around the circuit; a 12 V car battery, 12 J per coulomb. In the point-charge picture, it’s the work per unit charge from infinity to the point in question. Voltage is energy bookkeeping per charge — which is why multiplying volts by charge (or by current × time) always lands back on energy.

Why don’t birds get shocked on power lines?

Because both feet touch the same wire at the same potential — no potential difference across the bird means no current through it (the wire’s own resistance creates a minuscule drop per foot-span, far below harm). The danger is bridging two potentials: wire-to-pole or wire-to-wire contact. It’s the cleanest everyday demonstration that current follows potential differences, not potential itself — 100 kV of height is harmless; a few volts across the wrong path (wet skin, a heart) need not be.

Is this electric potential calculator free?

Yes — free, instant, no sign-up. Enter source charge and distance for V in volts/kV, the test charge’s energy, and the field strength at the same point for scale.