Camera angle of view calculator
Shows how much of a scene a lens takes in: a 50 mm focal length across a 36 mm sensor width covers 39.597752709 degrees. Use the width, height or diagonal, in the same unit as the focal length. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Sensor dimension
- 36
- Focal length
- 50
- Angle of view degrees
- 39.597752709
- Angle of view radians
- 0.6911111612
A camera lens does not have one fixed angle of view by itself: the visible angle depends on both focal length and the physical sensor dimension being measured. This calculator applies the standard rectilinear relation to one sensor width, height, or diagonal, provided in the same unit as the focal length. It returns the resulting angle in degrees and radians, making it useful for photography planning, cinematography, machine vision, technical documentation, and repeatable application workflows.
Choose the sensor dimension that matches your question
Angle of view can describe the horizontal, vertical, or diagonal span of an image, so begin by deciding which physical sensor dimension answers your question. Enter sensor width for horizontal framing, sensor height for vertical framing, or the sensor diagonal for the diagonal figure commonly printed in specifications. The calculator intentionally accepts one dimension rather than assuming an aspect ratio, which makes it useful for unusual sensors, cropped readout modes, film gates, scanning backs, and machine-vision cameras as well as familiar photographic formats.
Enter focal length in exactly the same unit as the selected dimension. Millimetres are conventional, but centimetres or inches work equally well when both numbers use that unit because their ratio is dimensionless. Use the actual active imaging dimension when a camera crops its sensor for video or stabilization; the nominal full sensor size would describe a wider angle than the recorded frame.
Both values must be positive finite numbers.
Apply the result with the model's limits in mind
Use the calculated angle to compare lenses on one camera, match framing across different sensor formats, estimate whether a machine-vision camera covers a target area, or configure a virtual camera. For a complete three-axis specification, run the calculator separately with sensor width, height, and diagonal while keeping focal length unchanged. The result represents the standard rectilinear thin-lens model.
It does not correct optical distortion, fisheye projection, focus breathing, internal focusing, lens pupil position, digital stabilization crops, or manufacturer-specific image processing. Real lenses can therefore differ slightly, especially near the frame edges, at close focus, or at extreme focal lengths. Treat manufacturer measurements or calibrated test images as authoritative when tolerances affect safety, metrology, or expensive production decisions.
For ordinary planning and comparison, the formula supplies the conventional angle quoted in optical references. Keep the chosen dimension explicit in your surrounding data because the numerical output alone cannot reveal whether it represents a horizontal, vertical, or diagonal angle. Clear labels prevent technically correct numbers from being applied to the wrong framing axis.
What you can do with it
Compare lens framing
Calculate the horizontal or vertical angle for several focal lengths before choosing which lenses to carry or rent.
Configure machine vision
Turn a camera sensor dimension and focal length into an angular coverage value for inspection and monitoring layouts.
Match physical and virtual cameras
Supply an angle in radians or degrees to previs, rendering, and simulation tools that must reproduce a real camera setup.
FAQ
Which sensor dimension should I enter?
Use sensor width for horizontal angle, sensor height for vertical angle, or sensor diagonal for diagonal angle of view.
What formula does the calculator use?
It uses twice the inverse tangent relation: 2 × atan(sensor dimension ÷ (2 × focal length)).
Does it model fisheye lenses or distortion?
No. The result follows the standard rectilinear thin-lens model and does not apply a distortion or fisheye projection.
What is the angle of view of a 50 mm lens on a 36 mm wide sensor?
39.597752709 degrees horizontally: twice the arctangent of 36 divided by twice 50. Enter the sensor height or diagonal instead to get the vertical or diagonal angle.
Why does a cropped video mode narrow the angle of view?
Because the camera records from a smaller part of the sensor. Enter the active imaging dimension, not the nominal sensor size, or the result will describe a wider view than the recorded frame.
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/optics/camera-angle-of-view \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"sensor_dimension":36,"focal_length":50}'const res = await fetch("https://api.kit.forhosting.com/optics/camera-angle-of-view", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"sensor_dimension": 36,
"focal_length": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/optics/camera-angle-of-view",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"sensor_dimension": 36,
"focal_length": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/camera-angle-of-view", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"sensor_dimension":36,"focal_length":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"sensor_dimension":36,"focal_length":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/camera-angle-of-view", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"sensor_dimension": 36,
"focal_length": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "optics.camera_angle_of_view",
"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
Browser calculations are immediate, while each successful API item costs $0.002.
Choose the sensor dimension that matches your question
Zero, negative values, missing fields, and malformed numeric text return an invalid_input error instead of producing a misleading result. Aliases are accepted for convenient API integration, but the canonical field names are sensor_dimension and focal_length.
Understand the twice-arctangent calculation
The calculation uses angle of view equals two times the inverse tangent of sensor dimension divided by twice the focal length. Geometrically, half of the sensor dimension and the focal length form the opposite and adjacent sides of a right triangle measured from the optical axis to one frame edge. The inverse tangent gives the half-angle, and multiplying by two covers the complete span from one edge to the other. A larger sensor dimension increases the angle for a fixed focal length, while a longer focal length narrows it for a fixed sensor. The response includes angle_of_view_degrees for lens comparisons and human-readable plans, plus angle_of_view_radians for graphics, simulation, computer vision, and other mathematical software. It also echoes the normalized inputs and supplies the formula label so stored results remain understandable.
Apply the result with the model's limits in mind
The free browser calculation is convenient for individual checks, while API calls at $0.002 per successful item fit catalog builders, rental tools, shot planners, and validation pipelines.
Technical questions
Do the values have to be in millimetres?
No. Any length unit works, provided sensor_dimension and focal_length use the same unit.
How much does an API calculation cost?
Each successful API item costs $0.002. The browser calculator is available for immediate interactive checks.