Miter angle calculator
A square 90 degree corner takes a 45 degree cut on each piece, a hexagon planter 30 degrees and an octagon frame 22.5. Enter the corner you measured to get the saw setting even when a wall is out of square. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Corner angle
- 90
- Sides
- 4
- Blade angle
- 45 deg
- Cut angle
- 45
- Exterior angle
- 90
- Polygon miter deg
- 45
This miter angle calculator converts a measured interior corner and the number of sides of a frame or box into the blade angle you set on a miter saw so two boards close without a gap. Carpenters, trim installers, and weekend builders need that saw setting because a square ninety-degree corner takes a forty-five-degree cut on each piece, a hexagonal planter takes thirty degrees, and an octagonal frame takes twenty-two and a half, while a wall that is two degrees out of square needs a slightly different dial than the textbook polygon. Enter the interior corner in degrees and the number of equal sides; the engine returns the miter-saw blade angle as half the supplement of the corner, plus the regular-polygon miter of one hundred eighty divided by the side count so you can compare a measured joint with a perfect n-gon.
What a miter saw blade angle is and how two boards close a corner
The miter saw blade angle is the number you set on the saw's miter gauge so two boards meet at a chosen interior corner without a gap. On a typical saw, zero degrees is a square crosscut, ninety degrees to the fence; the familiar picture-frame joint is forty-five degrees on each piece because a ninety-degree interior corner splits evenly.
A hexagonal interior of one hundred twenty degrees therefore needs a thirty-degree saw setting; an octagonal interior of one hundred thirty-five needs twenty-two and a half; an acute sixty-degree decorative corner needs sixty degrees on the dial, which many saws cannot reach without a jig. The number of sides of the finished frame still matters.
For a regular n-gon the interior is ((n minus 2) times 180) divided by n and the textbook miter is 180 divided by n, which matches the two-board formula exactly when the measured corner is that regular interior. When a wall is out of square you keep the measured corner for the actual cut and still report 180 divided by n so you can see the delta.
FAQ
What miter do I use for a square picture frame or a hexagon planter?
A regular octagon is 135 and 8, which yields 22.5.
What miter angle do I cut for a corner that is not 90 degrees?
Subtract the measured corner from 180 and split the difference between the two boards. A 120 degree corner gives 30 degrees on each piece, and a 135 degree corner gives 22.5.
Why does the result also show 180 divided by the number of sides?
That is the miter of a perfect shape with that many equal sides. Comparing it with the cut for your measured corner shows how far your joint is from the textbook polygon.
Does it work for crown molding?
No. It gives the flat miter setting for two boards meeting at one corner. Compound bevels for crown molding, spring angles and the width of the saw blade are not part of the calculation.
Which corners can I enter?
Any interior corner strictly between 0 and 180 degrees. A straight line or a corner wider than 180 degrees cannot be closed by two boards, so those values are not accepted.
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/build/miter-angle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"corner_angle":90,"sides":4}'const res = await fetch("https://api.kit.forhosting.com/build/miter-angle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"corner_angle": 90,
"sides": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/build/miter-angle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"corner_angle": 90,
"sides": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/build/miter-angle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"corner_angle":90,"sides":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"corner_angle":90,"sides":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/build/miter-angle", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"corner_angle": 90,
"sides": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "build.miter_angle",
"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
The corner must sit strictly between zero and one hundred eighty degrees: a zero, straight, or reflex angle cannot form a two-board miter, so those requests fail with invalid_input instead of a hollow zero.
What a miter saw blade angle is and how two boards close a corner
The same split works for any interior corner strictly between zero and one hundred eighty degrees: the exterior turn at the joint is one hundred eighty minus the corner, and each of the two mating boards takes half of that turn, so blade_angle equals (180 minus corner_angle) divided by two. This page does not compute compound crown-molding bevels, spring angles, or kerf compensation; it answers the flat miter dial for two boards at one corner of an n-sided joint, with stable numeric output suitable for cut lists, shop displays, and API consumers that must not invent a saw setting.
Input contract, response shape, and error behaviour
Sides below two or above three hundred sixty, and non-integers, are rejected the same way. Failed validation is not billed. POST a JSON body with two required fields: corner_angle, a finite number of degrees strictly between zero and one hundred eighty, with aliases angle, interior_angle, interior, corner, and included_angle; and sides, an integer from two through three hundred sixty for the equal pieces in the frame or closed joint, with aliases n, pieces, count, number_of_sides, and num_sides. An optional precision field, with aliases decimals and dp, chooses how many decimal places to publish, defaulting to six and capped at fifteen so JSON goldens stay stable across runtimes. Missing fields, empty strings, non-numeric tokens, and non-finite values fail with invalid_input that names the field. On success the body echoes the parsed corner_angle and sides, returns blade_angle as the primary saw setting, cut_angle as half the interior (the angle on the workpiece), exterior_angle as one hundred eighty minus the corner, and polygon_miter_deg as one hundred eighty divided by sides. When sides is at least three the body also includes regular_interior_deg and out_of_square_deg so an out-of-plumb wall is visible as a signed delta from the regular n-gon. Example: corner_angle ninety and sides four yields blade_angle forty-five, matching both the two-board split and the square-frame miter of 180/4.
Where a miter-angle API earns its keep in the shop and in software
Typical framing and trim examples are easy to check by hand: a square room corner is ninety over two boards, forty-five on the saw; a regular hexagon planter is one hundred twenty interior and six sides, thirty on the saw; a regular octagon window is one hundred thirty-five and eight sides, twenty-two and a half. Estimating tools embed the contract so a schedule of corners and side counts becomes a cut list without a spreadsheet of mixed formulas. Pair it with board-foot or drywall helpers when you are building a small lab of free, deterministic shop tools, and always cut a scrap before the good stock. Keep both pieces at the same blade_angle and flip the second board so the long points meet; that is the whole shop method this number supports. When a digital angle finder reads ninety-two instead of ninety, send that measured corner with sides four and use blade_angle forty-four rather than the textbook forty-five, then read out_of_square_deg as the two-degree error. Classroom and apprenticeship worksheets can pair a success case with a corner of one hundred ninety so learners see the hard invalid_input path instead of a silent clamp. This is not a birdsmouth seat-and-plumb calculator, not a roof-pitch slope, and not a compound crown engine: those are different search intents with different inputs. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split—free interactive exploration and a priced, identical API—lets you move from a phone check at the saw to an automated pipeline without changing the mathematical result.
Integration use cases
Picture frames and equal-sided boxes
Set corner_angle to the interior of each joint and sides to four, six, or eight so a square, hexagon, or octagon frame gets a matching miter on every end.
Out-of-square trim and baseboard
Measure the real wall corner with an angle finder, send that value with sides of the run, and use blade_angle instead of a 45° detent so the joint closes.
Estimating software and cut lists
Call the API from a take-off tool to turn a schedule of corners and side counts into reproducible saw settings without re-implementing the split in every client.
Technical questions
How do I calculate the miter saw blade angle from a corner and the number of sides?
Send a finite corner_angle strictly between 0 and 180 degrees and an integer sides from 2 to 360. The API returns blade_angle = (180 − corner_angle) / 2 as the saw setting for two boards, plus polygon_miter_deg = 180 / sides for the regular n-gon.
What happens if the corner angle is not between 0 and 180 degrees?
The task fails with invalid_input. A zero, straight, or reflex corner cannot form a two-board miter, and the request is not billed.
Why do I need both the corner angle and the number of sides?
The corner is the measured interior of this joint and drives blade_angle. The side count is the frame or polygon you are building and drives polygon_miter_deg and, when sides ≥ 3, the regular interior so out-of-square walls show as a delta.
What does the miter angle calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.