Magnetic force calculator
A charge of 0.002 C crossing a 0.5 T field at 500,000 m/s feels 500 N: enter the charge, its speed, the field and the angle between motion and field to get the magnetic force on that moving charge. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Charge
- 0.002
- Velocity
- 500,000
- Magnetic field
- 0.5
- Angle
- 90
- Angle rad
- 1.5707963268 N
- Sin theta
- 1
- Force
- 500
- Force N
- 500
The magnetic part of the Lorentz force on a point charge moving through a uniform magnetic field is one of the core results of classical electromagnetism: the force magnitude equals the product of the absolute charge, the speed, the field strength, and the sine of the angle between the velocity vector and the magnetic field. Students use F equals q v B sin theta to convert microcoulomb lab charges and laboratory-scale tesla fields into newton-scale forces, and engineers use the same product as a first-order estimate for beam deflection, current-carrying wire loads, and Hall-effect geometry before full multiphysics solvers. This magnetic force calculator accepts a finite charge in coulombs, a non-negative velocity in meters per second, a non-negative magnetic field in tesla, and an angle in degrees restricted to the closed interval from zero to one hundred eighty. It multiplies by the sine of that angle with deterministic floating-point arithmetic and returns the force magnitude in newtons together with cleaned inputs, the angle in radians, the sine value, and a short printable expression. Angles outside zero through one hundred eighty are rejected with a clear validation error so radian mistakes and non-physical inputs never silently produce a wrong answer.
How the Lorentz magnetic force formula works
The full Lorentz force on a charge q is q times E plus q times v cross B. When only the magnetic contribution matters, or when E is zero, the magnitude of the magnetic force reduces to F equals absolute q times v times B times sin of theta, where theta is the angle between the velocity vector and the magnetic field vector.
In SI units q is in coulombs, v is in meters per second, B is in tesla, theta is dimensionless as an angle, and F is in newtons. The sine factor means the force is zero when the charge moves parallel or anti-parallel to the field (theta equals zero or one hundred eighty degrees) and reaches its maximum when motion is perpendicular to B (theta equals ninety degrees). That is why cathode-ray tubes, mass spectrometers, and cyclotron paths care so much about the orientation of v relative to B.
This capability computes only the scalar magnitude, using the absolute value of q so homework answers that ask for how large the force is stay non-negative regardless of polarity. Vector direction via the right-hand rule, the electric term qE, relativistic corrections, and force on a current-carrying wire segment I L cross B are separate search intents and belong on separate landings.
Angles outside the closed interval from zero to one hundred eighty degrees are refused with invalid input instead of wrapping or taking an absolute value that would hide a unit error.
What you can do with it
Homework and lab Lorentz force drills
Compute F = |q| v B sin(θ) for textbook charges, speeds, fields, and angles so teachers and auto-graders share one ground truth including out-of-range angle errors.
First-pass beam and magnet estimates
Estimate magnetic force magnitude on a moving charge in a uniform field before full particle-tracking or multiphysics simulation.
FAQ
What formula does this magnetic force calculator use?
The Lorentz magnetic force magnitude F = |q| v B sin(θ) with q in coulombs, v in m/s, B in tesla, θ in degrees (0..180), and F in newtons.
What happens if the angle is outside 0..180?
The angle between velocity and magnetic field must be between 0 and 180 degrees inclusive; values outside that range are rejected rather than wrapped.
Does the sign of the charge matter?
The magnitude uses |q|, so F is always non-negative. The signed charge is still echoed in the response for your records. Direction (right-hand rule) is a vector question not covered here.
What units should I use?
SI only: charge in coulombs, velocity in m/s, magnetic field in tesla, angle in degrees.
What does it cost?
The browser tool is free and runs locally.
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/magnetic-force-charge \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"charge":0.002,"velocity":500000,"magnetic_field":0.5,"angle":90}'const res = await fetch("https://api.kit.forhosting.com/elec/magnetic-force-charge", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"charge": 0.002,
"velocity": 500000,
"magnetic_field": 0.5,
"angle": 90
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/elec/magnetic-force-charge",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"charge": 0.002,
"velocity": 500000,
"magnetic_field": 0.5,
"angle": 90
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/elec/magnetic-force-charge", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"charge":0.002,"velocity":500000,"magnetic_field":0.5,"angle":90}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"charge":0.002,"velocity":500000,"magnetic_field":0.5,"angle":90}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/elec/magnetic-force-charge", 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": 0.002,
"velocity": 500000,
"magnetic_field": 0.5,
"angle": 90
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "elec.magnetic_force_charge",
"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
What you send and what you get back
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 two millicoulombs at five times ten to the five meters per second in a half-tesla field at ninety degrees, a parallel-motion case at zero degrees that must yield zero force, and an angle of two hundred degrees that must error. If you need vector force components, the electric Lorentz term, wire force I L B sin theta, or cyclotron radius formulas, treat those as separate tools rather than extending this pure magnitude product. Send a finite charge under the field charge expressed in coulombs, a finite non-negative velocity under velocity in meters per second, a finite non-negative magnetic field under magnetic_field in tesla, and a finite angle under angle in degrees between zero and one hundred eighty inclusive. The same charge is accepted under the aliases q, Q, or coulombs; velocity under v, speed, or meters_per_second; magnetic field under B, b, tesla, or field; and angle under theta, degrees, or angle_deg, but only one key may appear for each quantity in a request. Angle must lie in the closed interval from zero through one hundred eighty; values below zero or above one hundred eighty, NaN, Infinity, negative velocity, and negative field fail with invalid_input and are not charged. On success the response includes cleaned charge, velocity, magnetic_field, and angle, angle_rad as the same angle in radians, sin_theta as the sine used in the product, force and force_N as the same magnitude in newtons, unit set to N, a short expression string showing absolute q, v, B, the angle in degrees, and the result, method lorentz_magnetic_force, and the formula string F equals absolute q v B sin of theta. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where magnetic force calculators show up in real work
Introductory physics and electrical-engineering courses constantly assign q v B sin theta drills so students can convert between laboratory charges, beam speeds, and tesla-scale fields before they move on to flux and Faraday induction. Beamline and vacuum-system teams estimate magnetic deflection forces on charged particles as a first pass before full particle-tracking simulation, using a single uniform-field model when geometry is simple. Keep vector Lorentz, electric-plus-magnetic, wire-force, and cyclotron-radius 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 labs that place a known charge at a known speed in a calibrated magnet can call the API and assert that the expected newton force matches probe or balance 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 instrument fixture checks
Bulk-generate expected newton values for known q, v, B, and θ in contest fixtures, worksheets, and lab magnet calibration tables.