Vertical angle of view calculator
A 50 mm lens on a 24 mm tall full-frame sensor sees about 27 degrees from top to bottom: enter the focal length and sensor height to check whether a facade or a standing figure fits. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Focal length
- 50
- Sensor height
- 24
- Vertical aov deg
- 26.9914665616
- Vertical aov rad
- 0.4710899614
- Half angle deg
- 13.4957332808
The vertical angle of view is the up-and-down field angle a rectilinear lens records on a given imaging rectangle. Photographers who frame towers, trees, statues, and standing portraits need this number more than the horizontal or diagonal angles that general field-of-view pages report. This vertical angle of view calculator takes lens focal length and physical sensor height in the same length unit—almost always millimetres—and returns the vertical field angle in degrees from the closed-form identity two times arctangent of height over two times focal length. An optional subject distance yields the vertical scene coverage so you can check whether a facade or a full-length figure still fits at the working distance you can actually stand.
How vertical angle of view is computed
The vertical angle of view of a rectilinear lens is a geometry problem, not a brand-specific secret. Place the thin lens at the origin and the sensor a focal length behind it. The top and bottom of the imaging rectangle sit at plus and minus half the sensor height from the optical axis.
The ray from the lens centre through each of those edges makes an angle whose tangent is half-height over focal length, so the full vertical field is two times the arctangent of sensor height over two times focal length. Convert radians to degrees by multiplying by one hundred eighty over pi. A fifty millimetre lens on a twenty-four millimetre tall full-frame sensor therefore sees about twenty-seven degrees vertically; the same lens on a fifteen-point-six millimetre APS-C sensor sees a narrower slice.
Zooming in—lengthening focal length—shrinks the angle; swapping to a taller sensor or rotating a rectangular sensor to portrait so the long side becomes the vertical dimension widens it. The model assumes a rectilinear projection with no barrel or fisheye mapping; those projections need a different formula and are outside this tool. Units cancel: millimetres over millimetres, or inches over inches, give the same angle.
Composing tall subjects, buildings, and standing figures
Architectural and real-estate photographers live on vertical angle of view when a facade must fit from the sidewalk they are allowed to stand on. Enter the lens you actually have, the sensor height of the body in the orientation you will shoot, and the distance to the building line; the coverage figure tells you whether the roofline still clears the frame or whether you need a wider prime, a taller sensor, or a step back.
Portrait and fashion teams use the same number to keep a standing figure from clipping at the feet when they lock a eighty-five millimetre look and cannot retreat. Tree, waterfall, and slot-canyon shooters plan the same way: the vertical slice is what makes or breaks the composition, not the horizontal width of the valley. Firmware authors, camera-simulation games, and location-scouting apps encode the same two-arctan rule when previewing whether a kit still covers a cathedral nave after a body swap.
If you later need the three-axis horizontal-plus-vertical-plus-diagonal field of view, crop-factor equivalent focal length, or depth of field, treat those as separate search intents and landings rather than overloading this vertical angle of view calculator page.
What you can do with it
Fit a building from the sidewalk
Enter focal length, the sensor height in the orientation you will shoot, and the distance to the facade to see whether the roofline still clears the frame.
Standing portraits without clipped feet
Lock an eighty-five millimetre look and check vertical coverage at the working distance so a full-length figure still fits without stepping back.
FAQ
Why is vertical AOV different from horizontal or diagonal field of view?
Each angle uses a different sensor dimension. Vertical AOV uses only the height of the frame—the axis that decides whether a tower, tree, or standing person fits. Horizontal uses width; diagonal uses the Pythagorean hypotenuse.
What sensor height should I enter for full-frame, APS-C, or Micro Four Thirds?
Use the physical height of the imaging rectangle: about 24 mm for full-frame landscape, 15.6 mm for typical APS-C, and 13 mm for Micro Four Thirds. In portrait orientation, swap in the long side (36 mm on full frame).
What does the vertical angle of view calculator cost?
The browser tool is free and runs locally.
What is the vertical angle of view of a 50 mm lens on full frame?
About 27 degrees. A full-frame sensor is 24 mm tall, and with a 50 mm focal length the lens covers that much of the scene from top to bottom when you hold the camera in landscape orientation.
Can I check whether a building fits from where I stand?
Yes. Add the optional subject distance and the result also shows how tall a slice of the scene the frame covers at that distance, so you can see whether a facade or a full figure fits.
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/hobby/photo-vertical-angle-of-view \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"focal_length":50,"sensor_height":24}'const res = await fetch("https://api.kit.forhosting.com/hobby/photo-vertical-angle-of-view", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"focal_length": 50,
"sensor_height": 24
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/hobby/photo-vertical-angle-of-view",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"focal_length": 50,
"sensor_height": 24
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/hobby/photo-vertical-angle-of-view", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"focal_length":50,"sensor_height":24}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"focal_length":50,"sensor_height":24}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/hobby/photo-vertical-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
{
"focal_length": 50,
"sensor_height": 24
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "hobby.photo_vertical_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
Invalid zeros, negatives, and non-finite values fail with invalid_input.
How vertical angle of view is computed
Zero or negative focal length would divide by zero or invert the camera, so those inputs are rejected as invalid_input rather than returning Infinity.
What you send and what you get back
Typical photographic values are millimetres—fifty and twenty-four for a standard prime on full frame, twenty-four and fifteen-point-six for a wide prime on APS-C. A classic check is fifty millimetres on twenty-four millimetres of height, which yields about twenty-six point nine nine degrees. Wire the free browser form for field math, then call the identical contract from scripts when you bulk-build lens tables or lesson answer keys. Send two required fields that share one length unit: focal_length for the lens and sensor_height for the physical height of the imaging rectangle along the vertical frame axis. When the camera is rotated to portrait, pass the long side as sensor_height so the calculator describes the tall axis you are actually composing. Aliases such as focal, f, fl, height, sensor_h, h, and frame_height are accepted when documented so forms and SDK demos stay flexible. An optional subject_distance, in whatever unit you want coverage reported in, returns vertical_coverage equal to distance times height over focal length, which is the similar-triangles height of the scene that fills the frame. Missing fields, non-numeric strings, negative sizes, and zero or non-positive focal length all fail with invalid_input and are not billed. On success the response echoes cleaned focal_length and sensor_height, vertical_aov_deg and vertical_aov_rad, half_angle_deg for tilt planning, plus formula, method, and unit_note strings for display and tests. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Composing tall subjects, buildings, and standing figures
Photography courses assign vertical-AOV word problems constantly—convert millimetres to degrees, then to metres of coverage at a stated distance—so a deterministic API speeds grading and demo setup. 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
Classroom vertical-AOV drills
Generate answer keys for millimetres-to-degrees and coverage-at-distance problems with stable vertical_aov_deg values for auto-graders.
Technical questions
How do I calculate vertical angle of view from focal length and sensor height?
Send focal_length and sensor_height in the same unit (typically millimetres). The tool returns vertical_aov_deg = 2 × atan(sensor_height / (2 × focal_length)) converted to degrees, plus the same angle in radians.
How do I use this when photographing a tall building?
Pass the lens you have, the sensor height in the orientation you will shoot (the long side if the camera is portrait), and optionally the distance to the facade. vertical_coverage is the scene height that fills the frame at that stand-off.