Electric dipole calculator
Halve the distance to a dipole and the field on its axis grows eight times, while the potential grows four times. Enter the dipole moment in coulomb-metres and the distance in metres, then choose field or potential. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Dipole moment
- 0.000000001
- Distance
- 0.1
- Quantity
- Field
- Value
- 17,975.1035846 N/C
- K
- 8,987,551,792.3
- Electric field
- 17,975.1035846
- Equation
- E = 2 × 8987551792.3 × 1e-9 / (0.1)³ = 17975.1035846
An electric dipole is a pair of equal and opposite charges summarized by a single vector: the electric dipole moment p, measured in coulomb-metres. On the axial line of an ideal dipole the electric field falls as one over r cubed and the electric potential falls as one over r squared, both scaled by Coulomb's constant k. This calculator takes that dipole moment and the axial distance from the dipole centre, then returns either the axial field strength in newtons per coulomb or the axial potential in volts.
What an axial electric dipole is and how E and V are computed
An electric dipole is the simplest electrostatic multipole after a point charge: two equal and opposite charges of magnitude q separated by a vector of length l, summarized by the dipole moment p equals q times l, in coulomb-metres.
On the axial line of an ideal dipole, or in the far-field limit where the observation distance r is much larger than the charge separation, the electric field points along the axis and has magnitude E equals two k p over r cubed, while the electric potential with respect to infinity is V equals k p over r squared. Here k is Coulomb's constant, about eight point nine eight seven six times ten to the nine newton metre squared per coulomb squared, the same constant used for a point-charge field.
The one-over-r-cubed field and the one-over-r-squared potential are the signatures that distinguish a dipole from a monopole, whose field falls as one over r squared. The sign of p is kept: a positive moment pointing toward the observation point yields a positive axial field and a positive potential; reversing the dipole flips both signs. This calculator evaluates those two axial identities from p and r.
Zero dipole moment is allowed and returns a zero field or a zero potential. Distance, however, must be strictly greater than zero, because both formulas divide by a positive power of r and a vanishing or negative axial coordinate is not a physical observation point on the axis of the dipole.
Where an electric dipole calculator earns its keep
Classrooms and tutoring platforms use an electric dipole calculator so learners can check E equals two k p over r cubed and V equals k p over r squared for arbitrary SI pairs without dropping a power of ten on centimetres or nanocoulomb-metres. Molecular and materials notebooks convert a tabulated dipole moment into an on-axis field or potential at a stated distance when sketching a first electrostatic estimate before a full multipole or quantum calculation.
Prefer this landing when you already have the dipole moment in coulomb-metres and you want the far-field axial formulas; if you have a single point charge rather than a dipole, use a point-charge field or potential identity instead, because those fall as one over r squared and one over r. Equatorial points, finite dipole length, and higher multipoles are outside this contract, so treat the result as the classic axial baseline rather than a three-dimensional extraction. Failed validation does not consume balance.
Keep classroom centimetre axes and nanocoulomb-metre moments inside ordinary SI magnitudes, pin the rounded field or potential in tests, and you get reproducible electrostatic arithmetic for homework, LMS plugins, and edge workers without standing up a field solver of your own.
What you can do with it
Molecular and sensor first estimates
Notebooks convert a tabulated dipole moment into an on-axis field or potential at a stated distance before running a full multipole or laboratory measurement.
Curriculum and auto-graded drills
Lesson builders produce SI-unit axial dipole checks for demos, LMS items, and lab write-ups without embedding an electromagnetic solver.
FAQ
How do I calculate the axial electric potential of a dipole?
Send the same p and r with quantity "potential".
What units does the electric dipole calculator use?
SI units: dipole moment in coulomb-metres, axial distance in metres, field in N/C, potential in volts. Convert debye or centimetres to SI before calling.
Why does a dipole's field fall off faster than a single charge's?
Because the two opposite charges partly cancel when seen from a distance. On the axis the field drops with the cube of the distance and the potential with its square, while the field of a single charge drops only with the square.
Does it work for points beside the dipole rather than on its axis?
No. It works only along the axis and treats the dipole as ideal, with no charge spacing to enter. On the perpendicular midline the potential of an ideal dipole is zero and the field has another form, which this calculator does not give.
My data sheet gives the moment in debye. What should I do?
Convert it to coulomb-metres before entering it, because the calculator does not convert units. Then give the distance in metres to get the field in newtons per coulomb or the potential in volts.
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/phys/dipole \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"dipole_moment":1e-9,"distance":0.1}'const res = await fetch("https://api.kit.forhosting.com/phys/dipole", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"dipole_moment": 1e-9,
"distance": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/dipole",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"dipole_moment": 1e-9,
"distance": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/dipole", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"dipole_moment":1e-9,"distance":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"dipole_moment":1e-9,"distance":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/dipole", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"dipole_moment": 1e-9,
"distance": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.dipole",
"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
Distance must be strictly positive: zero or negative separation is rejected as invalid_input because both formulas divide by a power of r.
What an axial electric dipole is and how E and V are computed
It does not model the equatorial line, where the potential of an ideal dipole is zero and the field is minus k p over r cubed, and it does not keep a finite charge-separation length as a third input, because the request is the two-parameter far-field axial problem.
Input contract, quantity choice, response shape, and errors
When quantity is omitted the engine defaults to field, which is the more common homework request. Optional output keys that do not apply are omitted rather than set to null. Convert debye to coulomb-metres yourself before calling if your data sheet uses debye. POST a JSON body with two required finite numbers and an optional quantity flag. dipole_moment is the electric dipole moment p in coulomb-metres; aliases p, moment, and electric_dipole_moment are accepted. distance is the axial distance r from the dipole centre in metres; aliases r, axial_distance, and meters are accepted. quantity selects which axial result to return: field for electric field strength E equals two k p over r cubed in newtons per coulomb, or potential for electric potential V equals k p over r squared in volts. Each numeric field may arrive as a JSON number or as a numeric string. Missing fields, empty strings, and non-finite values fail with invalid_input naming the field, and those failures are not billed. Distance must be strictly positive: zero distance makes both formulas divide by zero, and a negative distance does not describe a point on the axis, so both cases raise invalid_input with a message that axial distance cannot be zero or negative. An unknown quantity string is likewise invalid_input; the closed set is field or potential, not a free-text unit. On success the body echoes the rounded dipole moment and distance, the Coulomb constant k, the selected quantity, a primary value, the matching named field electric_field or electric_potential, the SI unit, a formula string, an equation string that substitutes the numbers, and method axial_dipole. A successful API call costs $0.002.
Where an electric dipole calculator earns its keep
Exam-prep generators need a deterministic oracle that marks a zero or negative axial distance as invalid_input instead of silently returning Infinity that a buggy grader might treat as success. Antenna and sensor notes sometimes treat a compact charge pair as an ideal dipole on axis; a tiny parse endpoint avoids pulling a field solver for that textbook baseline.
Integration use cases
Homework and exam verification
Students enter dipole moment and axial distance, compare N/C or volt results with hand work, and get a clear invalid_input when distance is zero or negative by mistake.
Technical questions
How do I calculate the axial electric field of a dipole?
Send dipole_moment p in C·m, distance r in metres, and quantity "field" (or omit quantity). The response includes electric_field from E = 2 k p / r³ in N/C.
What happens if axial distance is zero or negative?
The request fails with invalid_input. Zero or negative r makes E=2kp/r³ and V=kp/r² divide by a power of r, so the engine rejects it and does not charge the call.
What does the electric dipole calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.