Electric potential calculator
One microcoulomb seen from 10 centimetres sits at roughly 9 × 10⁴ volts, counted from zero at infinity. Enter the charge and the distance to get the potential of a point charge in volts, positive or negative like the charge itself. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Charge
- 0.000001
- Distance
- 0.1
- K
- 8,987,551,792.3 V
- Potential
- 89,875.517923
- Precision
- 10
This electric potential calculator returns the electrostatic potential of a single point charge at a chosen distance using the classic Coulomb formula V equals k times Q over r. Electric potential is the electric potential energy per unit charge relative to a reference, and for an isolated point charge in vacuum the reference is conventionally zero at infinity, which yields the compact closed form used here. You supply the charge Q and the radial distance r from the charge; the engine multiplies by Coulomb's constant k (default about 8.9875517923 times ten to the nine in SI) and divides by r to produce V in volts when inputs are consistent SI units. Distance zero is rejected because the potential of a point charge diverges at the charge itself. The path is pure finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
What electric potential means and what you get
Electric potential at a point is the work per unit positive test charge that would be required to bring that charge from the reference location to the point without kinetic energy changes, in the electrostatic approximation.
For a point charge Q sitting in free space, choosing the reference potential equal to zero at infinite distance produces the textbook formula V equals k Q over r, where r is the distance from the charge to the field point and k is Coulomb's constant equal to one over four pi epsilon zero in SI vacuum. The sign of V follows the sign of Q: a positive charge raises the potential nearby, and a negative charge lowers it.
This calculator does not integrate line charges, surface densities, or multipole expansions; it answers only the isolated point-charge case with a single radial distance. Zero charge is allowed and simply yields zero potential at every finite r. Negative distance is also rejected, since r is a radial separation, not a signed Cartesian coordinate.
Optional overrides of k let you use the common nine times ten to the nine textbook approximation or a media-adjusted constant when your course defines one.
Where point-charge potential checks fit in study, design, and software
Students meet V equals k Q over r when an electrostatics unit introduces potential before potential energy, when a lab asks for the potential at a measured distance from a charged sphere modeled as a point, or when a contest problem gives Q and r and asks for V without a full finite-element field solve. Teachers can pre-generate answer keys for modest charges and distances without trusting opaque calculator apps that silently mix microcoulombs with coulombs or switch reference points without saying so.
Developers call the same contract from scripts to seed deterministic test vectors for field visualizers, to normalize user-entered point charges before a rough shielding estimate, or to satisfy programming-challenge statements that demand volts rather than a hand-waved sketch. Makers and technicians use it for order-of-magnitude checks around charged surfaces when only a rough equivalent point charge and a standoff distance are known.
What you can do with it
Homework and lab checks
Compute V=kQ/r for textbook point charges before grading electrostatic potential worksheets or DC lab write-ups.
Design and order-of-magnitude checks
Estimate volts near an equivalent point charge when only Q and standoff distance r are known.
FAQ
What does the electric potential calculator cost?
It is free in your browser on this page.
Which formula does it use?
Default k is about 8.9875517923e9 in SI vacuum.
Can I change Coulomb's constant k?
Yes. Omit k to use the default SI value, or set k (for example 9e9) for a textbook approximation. k must be positive.
What units should I use?
Use a consistent set such as coulombs, metres, and N·m²/C² for k. Then potential is in volts (V). The tool does not convert prefixes for you.
Why can the electric potential be negative?
Because it keeps the sign of the charge. A positive charge raises the potential around it and a negative charge lowers it, so the same distance gives equal values with opposite signs.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/elec/electric-potential \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"charge":0.000001,"distance":0.1}'const res = await fetch("https://api.kit.forhosting.com/elec/electric-potential", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"charge": 0.000001,
"distance": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/electric-potential",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"charge": 0.000001,
"distance": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/electric-potential", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"charge":0.000001,"distance":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"charge":0.000001,"distance":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/electric-potential", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"charge": 0.000001,
"distance": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.electric_potential",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs_charge | 1000000000000000 |
max_abs_distance | 1000000000000000 |
max_abs_k | 100000000000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
What electric potential means here and what the response contains
The response returns the normalized charge, distance, and k used, the computed potential, the precision applied, a method tag electric_potential, a short formula reminder, and a unit hint V for SI-consistent inputs. Distance must be strictly positive: r equals zero makes the expression undefined and is rejected with invalid_input, because you would be evaluating the singular self-potential of a mathematical point charge.
How charge, distance, and k are read and how V stays reproducible
Each supplied value must be a finite decimal within the documented magnitude ceilings; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong voltage. Distance zero, distance below a tiny epsilon, or negative distance fails with a message that names the division-by-zero or positivity rule for V equals k Q over r. A non-positive custom k is rejected because Coulomb's constant in this model is a positive scalar. The preferred field for charge is charge, but aliases Q, q, coulomb, and coulombs are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Distance prefers distance, with aliases r, R, radius, and separation. Optional k prefers k, with aliases coulomb_constant, k_e, and ke; when omitted the engine uses the default SI vacuum constant about 8.9875517923e9. Missing charge or missing distance fails with invalid_input naming the field. An optional precision field, with aliases decimals and dp, chooses how many decimal places to expose for charge, distance, k, and potential, defaulting to ten and capped at fifteen so JSON goldens stay stable. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing Coulomb's potential yourself.
Where point-charge potential checks fit in study, design, and software
Product and education tools use the endpoint when a learner types charge and distance and the UI must show potential with a stable formula tag. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with energy or force helpers when you need related electrostatic steps, and with other physics endpoints when you are building a small lab of free, deterministic electricity calculators for study and software tests.
Integration use cases
Deterministic test fixtures
Generate reproducible potentials for unit tests, field demos, and CI assertions on the Coulomb potential formula.
Technical questions
What happens if distance is zero?
The input is rejected with invalid_input. At r = 0 the point-charge potential is undefined (division by zero).