Bolt circle calculator
Four holes on a 100 bolt circle centred at the origin, starting at 0°, land at (50, 0), (0, 50), (−50, 0) and (0, −50), 90° apart. Enter your flange or hub pattern and drill from the list. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Center x
- 0
- Center y
- 0
- Diameter
- 100
- Hole count
- 4
- Start angle
- 0
- Radius
- 50
- Angle step
- 90
- Angle unit
- deg
- Precision
- 8
A bolt circle, also called a pitch circle or bolt hole circle, is the circle that passes through the centers of equally spaced fastener holes on a flange, pulley, hub, or cover plate. Shop layout used to mean a protractor, a pair of dividers, and a second check that hole one really sat at the starting angle you marked. This bolt circle calculator takes the center coordinates, the circle diameter (the pitch-circle diameter, or PCD), the hole count, and the starting angle in degrees, then returns every hole as Cartesian x and y. The engine uses the standard polar identity: radius is half the diameter, the angular step is three hundred sixty degrees divided by the hole count, and hole i sits at start angle plus i times that step, with zero degrees along the positive x-axis and angles increasing counterclockwise.
What a bolt circle is and how the coordinates are formed
A bolt circle, pitch circle, or bolt hole circle is the circle whose circumference carries the centers of a regular pattern of fastener holes. Flanges, inspection covers, pulley bosses, wheel hubs, and rotary tables all use that pattern so every hole sits at the same radius and the same angular spacing from its neighbors. Zero degrees lies on the positive x-axis, which is three o'clock on a clock face drawn in the plane, and positive angles increase counterclockwise.
The first hole is numbered one in the response so shop-floor hole callouts match the array people write on a flange sketch. All linear quantities share one unit—millimeters, inches, or meters—because the engine never converts units for you. Angles are always degrees on the way in and degrees on the way out.
The work is deterministic: the same four numbers always produce the same hole list, with no Date, no randomness, and no network. If you need hole diameters, thread engagement, or eccentric bolt-group shear, those are different tools; this page answers only equally spaced center coordinates on a bolt circle.
Where a bolt circle calculator earns its keep
Fabricators meet this calculation when a pipe flange, a pump cover, or a gearbox inspection plate has to be drilled before the gasket is ordered, and a wrong first-hole angle wastes a plate. Wheel and pulley shops use the same numbers to drill hub patterns from a published PCD and hole count without transferring a paper template that has already stretched.
Students of mechanical drawing check that a four-hole pattern at zero degrees really lands on the axes, then rotate the start angle to match a clocked keyway or a slot that must clear a boss. Keep requests within one thousand holes, pin the rounded coordinates in tests, and you get reproducible hole lists for quotes, CAM posts, and homework without standing up a CAD kernel of your own.
Pair it with fastener or flange helpers when you are building a small lab of free, deterministic shop calculators, and keep engineering judgement for hole size, edge distance, and code-compliant connections that your drawing requires beyond the pure bolt-circle geometry.
What you can do with it
Flange and cover-plate layout
Convert center, pitch-circle diameter, hole count, and start angle into equally spaced hole XY before you drill a pipe flange or inspection cover.
Hub, pulley, and sprocket drilling
Lay out a published PCD bolt pattern on a wheel hub or pulley boss without a stretched paper template.
FAQ
Where is zero degrees, and do angles go clockwise?
Zero degrees is the positive X-axis (3 o'clock). Positive angles increase counterclockwise, matching CAD polar coordinates.
What happens if hole count is not a positive integer?
Zero, negative, and fractional hole counts cannot define an equally spaced bolt circle and are not billed.
Is diameter the pitch-circle diameter or the hole diameter?
Diameter is the pitch-circle diameter (PCD) that passes through the hole centers, not the diameter of the holes themselves. Linear units must match the center coordinates.
How do I put the first hole at twelve o'clock?
Enter a starting angle of 90 degrees. Zero degrees points along the positive x-axis, at three o'clock, and angles grow counterclockwise, so 90 places hole one straight up from the center.
What units are the hole coordinates in?
In millimetres, inches or metres, whichever you used when entering the pattern. Nothing is converted, and all angles are given in degrees, both in and out.
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/bolt-circle \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"center_x":0,"center_y":0,"diameter":100,"hole_count":4,"start_angle":0}'const res = await fetch("https://api.kit.forhosting.com/build/bolt-circle", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"center_x": 0,
"center_y": 0,
"diameter": 100,
"hole_count": 4,
"start_angle": 0
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/build/bolt-circle",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"center_x": 0,
"center_y": 0,
"diameter": 100,
"hole_count": 4,
"start_angle": 0
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/build/bolt-circle", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"center_x":0,"center_y":0,"diameter":100,"hole_count":4,"start_angle":0}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"center_x":0,"center_y":0,"diameter":100,"hole_count":4,"start_angle":0}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/build/bolt-circle", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"center_x": 0,
"center_y": 0,
"diameter": 100,
"hole_count": 4,
"start_angle": 0
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "build.bolt_circle",
"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.
Limits
max_holes | 1000 |
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
Hole count must be a positive integer; a zero, a fraction, or a negative value fails with invalid_input and is not billed.
What a bolt circle is and how the coordinates are formed
Given a center (center_x, center_y), a circle diameter, a hole count n, and a starting angle in degrees, the radius r is half the diameter and the angular step is 360 degrees divided by n. Hole i, counted from zero, sits at polar angle theta equal to start_angle plus i times 360 over n. Cartesian coordinates follow the standard identity x equals center_x plus r times cosine of theta and y equals center_y plus r times sine of theta, with theta converted to radians only inside the trigonometric call. That is the same convention used by most CAD systems and by the mathematical polar-to-Cartesian conversion; if your drawing places hole one at twelve o'clock, send start_angle as ninety. A four-hole pattern on a diameter of one hundred with center at the origin and start_angle zero produces holes at (50, 0), (0, 50), (−50, 0), and (0, −50), which is the classic cross that machinists use as a sanity check.
Input contract, response shape, and error behavior
A non-positive diameter is rejected because a bolt circle with zero or negative diameter cannot place holes at a real radius. A formula string restates the polar identity so you can audit a coordinate without reading source. POST a JSON body with five numbers. center_x and center_y locate the circle center in your drawing plane; they may be zero, negative, or large, and they accept aliases cx, centre_x and cy, centre_y. diameter is the pitch-circle diameter that passes through the hole centers, not the diameter of the holes themselves, and it must be a finite strictly positive number; aliases include d, pcd, bcd, circle_diameter, and pitch_diameter. hole_count is the number of equally spaced holes and must be a positive integer from one through one thousand; aliases include n, count, holes, and num_holes. start_angle is the polar angle of hole one in degrees, with aliases angle, theta, start, and starting_angle. Optional precision, with aliases decimals and dp, chooses decimal places for every numeric field in the response, defaulting to eight and capped at fifteen so JSON goldens stay stable across runtimes. Missing fields, empty strings, non-finite values, and magnitudes above the supported ceiling fail with invalid_input naming the field. A hole_count that is not a positive integer—zero, a negative number, a fraction such as four point five, or a non-numeric string—fails with a message that names hole_count and states that a positive integer is required; those failures are not billed. On success the body echoes the parsed center, diameter, radius, hole_count, start_angle, and angle_step, then lists holes as objects with a one-based index, a wrapped angle in degrees, x, and y. Pair the response with your own DXF or G-code writer if you need a drawing file; this endpoint returns coordinates only and does not emit plots, toolpaths, or fastener schedules.
Where a bolt circle calculator earns its keep
CNC programmers emit a bolt circle as a list of XY targets for a drill cycle, and a deterministic API beats a spreadsheet with mixed units and a hidden cell that still says four and a half holes. On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, nothing is stored after the response returns, and the mathematical result is identical.
Integration use cases
CNC and CAD fixture generation
Emit deterministic bolt-circle coordinates for a drill cycle, CAM post, or homework golden that must match the shop drawing.
Technical questions
How do I calculate equally spaced holes on a bolt circle?
Send center_x, center_y, diameter (PCD), hole_count, and start_angle in degrees. The API returns x = center_x + r cos(θ) and y = center_y + r sin(θ) for each hole, with r = diameter/2 and θ = start_angle + i × 360/n.
What does the bolt circle calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.