Electric field calculator
One microcoulomb seen from 10 centimetres gives a field of about 8.99 × 10⁵ N/C, and doubling the distance cuts it to a quarter. Enter the charge in coulombs and the distance in metres to get the field strength of one point charge. 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 N/C
- Electric field
- 898,755.17923
- Electric field N per C
- 898,755.17923
- Expression
- E = (8987551792.3) × |0.000001| / (0.1)² = 898755.17923 N/C
The electric field magnitude around an isolated point charge is one of the first quantitative results in electrostatics: E equals k times the absolute value of Q divided by the square of the radial distance r, with Coulomb constant k about 8.99 times ten to the nine newton metre squared per coulomb squared. Students use that inverse-square law to convert microcoulomb lab sources into newton-per-coulomb readings, and engineers use the same product as a first-order estimate before multipole expansions or full field solvers. Zero or negative distance is rejected with a clear validation error because the classical formula divides by r squared and distance is not physical below zero.
How the point-charge electric field formula works
Coulomb's law states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation. Dividing that force by a positive test charge yields the electric field of a single source charge Q: the magnitude is E equals k times absolute Q over r squared, directed radially outward for positive Q and inward for negative Q.
In SI units k is 8.9875517923 times ten to the nine newton metre squared per coulomb squared, Q is in coulombs, r is in meters, and E is in newtons per coulomb, numerically identical to volts per meter. The inverse-square dependence means doubling the distance quarters the field, which is why lab benches and high-voltage clearances care so much about geometry. This capability computes only the scalar magnitude, using the absolute value of Q so homework answers that ask for how strong the field is stay non-negative regardless of polarity.
Vector components, multi-charge superposition, line and surface distributions, and Gauss-law shells are separate search intents and belong on separate landings. At r equals zero the classical expression diverges; the calculator refuses that case with invalid input instead of emitting Infinity.
What you send and what you get back
Send a finite charge under the field charge, expressed in coulombs, and a finite positive distance under the field distance, expressed in meters. Numeric values and numeric strings are both accepted so form widgets and spreadsheet paste stay convenient; SI prefix strings such as one microcoulomb written as text are not parsed, so pass one times ten to the minus six for a microcoulomb source. Charge may be positive, negative, or zero.
Classic classroom checks include one microcoulomb at ten centimeters, two nanocoulombs at half a meter, and a zero-distance case that must error. If you need vector fields, multi-charge superpositions, continuous distributions, or Gauss-law shells, treat those as separate tools rather than extending this pure magnitude product.
What you can do with it
Homework and lab inverse-square drills
Compute E = k|Q|/r² for textbook point charges and distances so teachers and auto-graders share one ground truth including zero-distance errors.
First-pass high-voltage and ESD estimates
Estimate field magnitude near a charged object modeled as a point charge before full electrostatic simulation or probe measurement.
FAQ
What happens if distance is zero?
The classical formula divides by r², so zero distance is singular and is rejected rather than returning Infinity.
Does the sign of the charge matter?
The magnitude uses |Q|, so E is always non-negative. The signed charge is still echoed in the response for your records. Direction (inward vs outward) is a vector question not covered here.
What units should I use?
SI only: charge in coulombs, distance in meters.
What does it cost?
The browser tool is free and runs locally.
What happens to the field if I double the distance?
It drops to a quarter of its value. The field follows an inverse-square law, so it scales with one over the distance squared; halving the distance makes it four times stronger.
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-field-point \
-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-field-point", {
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-field-point",
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-field-point", 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-field-point", 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_field_point",
"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.
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
This electric field calculator accepts a finite charge in coulombs and a strictly positive distance in meters, multiplies by k, divides by r squared with deterministic floating-point arithmetic, and returns the field magnitude in newtons per coulomb together with cleaned inputs and a short printable expression.
What you send and what you get back
The same charge is accepted under the aliases q, Q, or coulombs, and distance under r, meters, or radius, but only one key may appear for each quantity in a request. Distance must be strictly greater than zero; NaN, Infinity, zero, and negative meters fail with invalid_input and are not charged. On success the response includes cleaned charge and distance, the constant k used, electric_field and electric_field_N_per_C as the same product, unit set to N/C, a short expression string showing k, absolute Q, r squared, and the result, method coulomb_point_charge, and the formula string E equals k absolute Q over r squared. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where electric field calculators show up in real work
Introductory physics and electrical-engineering courses constantly assign inverse-square field drills so students can convert between coulomb-scale sources and newton-per-coulomb readings before they move on to flux and potential. High-voltage and ESD teams estimate field strength near charged objects as a first pass before full electrostatic simulation, using a single point-charge model when geometry is simple. Keep multipole, continuous-distribution, and vector-field landings separate so each search intent has one clear page rather than an overloaded multi-formula tool that confuses both students and search engines. Instrumentation and sensor labs that place a known charge at a known spacing can call the API and assert that the expected magnitude matches probe readings within tolerance. Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Answer keys and sensor fixture checks
Bulk-generate expected N/C values for known Q and r in contest fixtures, worksheets, and lab sensor calibration tables.
Technical questions
What formula does this electric field calculator use?
The point-charge magnitude E = k|Q|/r² with k = 8.9875517923×10⁹ N·m²/C², Q in coulombs, r in meters, and E in N/C (equal to V/m).