Brinell hardness number calculator
A 3000 kgf load on a 10 mm ball that leaves a 3.4 mm impression gives about 320.583 HBW. Enter the load in kgf, N or lbf to see the depth, the contact area and whether the impression sits in the standard window. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Load
- 3,000
- Ball diameter
- 10
- Indent diameter
- 3.4
- Load unit
- Kgf HBW
- Length unit
- Mm
- Load kgf
- 3,000
- Ball diameter mm
- 10
The Brinell hardness test presses a hard spherical indenter into a metal surface under a known load and then measures the mean diameter of the remaining circular impression. The Brinell hardness number, written HBW or BHN, is that load divided by the curved surface area of the spherical cap left in the specimen. The area is not the flat circle of diameter d; it is the spherical surface π D h, which rearranges to the closed form two P over π D times the quantity D minus the square root of D squared minus d squared. This Brinell hardness number calculator accepts the applied load, the ball diameter, and the measured indentation diameter, converts optional force and length units into kilogram-force and millimetres, and returns HBW together with indentation depth, impression area, the load-to-diameter-squared ratio used to choose a standard test condition, and a flag for the ASTM recommended d over D window. Students check homework; foundry, forge, and heat-treat laboratories convert optical-microscope readings into HBW without a spreadsheet.
What Brinell hardness measures and how it is worked out
Johan August Brinell introduced the spherical-indentation hardness test in the early twentieth century so that a single number could rank steels, cast irons, and non-ferrous alloys by resistance to permanent plastic flow. A polished carbide ball of diameter D is forced into the specimen under a constant load P for a prescribed dwell, then the mean diameter d of the residual circular impression is measured with a microscope or optical scanner.
Hardness is defined as load per unit of the curved surface that actually contacted the ball, not per unit of the projected circle. That surface is a spherical cap of depth h equals one half of D minus the square root of D squared minus d squared, and its area is π D h. Dividing P by that area produces the familiar closed form HBW equals two P over π D times open parenthesis D minus the square root of D squared minus d squared close parenthesis.
When P is expressed in kilogram-force and both diameters in millimetres, the number has the historical dimension kgf per square millimetre; modern standards write it as HBW, the W recalling a tungsten-carbide ball, and no longer require a trailing unit. ASTM E10 and ISO 6506 further recommend that d lie between 0.24 D and 0.60 D so the impression is neither a pinprick (where diameter error explodes) nor an almost-hemispherical crater (where the ball is too soft or the load too high for the alloy).
Standard force-to-diameter-squared ratios of 1, 2.5, 5, 10, and 30 keep that window reachable across soft aluminium, copper alloys, and hardened steel. This calculator implements exactly that family of textbook and standards models: convert units, take one square root, divide, and report the auxiliaries a lab notebook usually writes beside the hardness number. It does not convert an already-known HBW into Rockwell or Vickers; that is a different search and a different capability.
Who relies on a Brinell hardness calculation
Foundry, forge, and heat-treat shops still run Brinell as the workhorse production test on castings, billets, and quenched-and-tempered bar because a ten millimetre ball averages over grain and graphite that would scatter a Rockwell point reading. Inspectors type the optical diameter into a bench terminal and need HBW, F over D squared, and a pass-or-warn on the d over D window without opening a spreadsheet that silently uses the projected-circle approximation P over π d squared over four.
University materials laboratories and exam generators need a deterministic oracle for the spherical-cap formula that also accepts newtons or inches, so students are graded on measurement and unit conversion rather than on who remembered the square-root identity. Content sites that rank for Brinell hardness number calculator, HBW from indentation diameter, BHN formula, or ASTM E10 hardness calculator benefit from a live free tool whose arithmetic matches the paid automation path byte-for-byte.
This page is not a hardness-scale converter: if you already have an HBW and want HRC or HV, that is a different query served by the scale-conversion capability. Invalid input is not billed.
What you can do with it
Foundry and heat-treat shop-floor readings
Convert a microscope impression diameter, ball size, and applied load into HBW, F/D², and a recommended-range flag before stamping a casting or heat-treat lot.
FAQ
How is the Brinell hardness number calculated?
Equivalently HBW = P / A where A = π D h is the spherical-cap area and h = (D − √(D² − d²)) / 2.
What units should I use for load and diameters?
The formula is evaluated in kgf and mm.
What is the recommended d/D range?
ASTM E10 and ISO 6506 recommend 0.24 ≤ d/D ≤ 0.60.
What does HBW 10/3000 mean?
It is the full Brinell designation: hardness measured with a 10 mm tungsten-carbide ball under a 3000 kgf load. The W recalls the carbide ball, and the calculator prints this label next to every result.
Is a reading outside the recommended range still calculated?
Yes. The hardness is still worked out, but a flag and a message warn that the standard would not accept it as an official test. The recommended impression lies between 0.24 and 0.60 times the ball diameter.
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/eng/brinell-number \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"load":3000,"ball_diameter":10,"indent_diameter":3.4}'const res = await fetch("https://api.kit.forhosting.com/eng/brinell-number", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"load": 3000,
"ball_diameter": 10,
"indent_diameter": 3.4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/brinell-number",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"load": 3000,
"ball_diameter": 10,
"indent_diameter": 3.4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/brinell-number", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"load":3000,"ball_diameter":10,"indent_diameter":3.4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"load":3000,"ball_diameter":10,"indent_diameter":3.4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/brinell-number", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"load": 3000,
"ball_diameter": 10,
"indent_diameter": 3.4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.brinell_number",
"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 input fails with invalid_input and is not billed.
Input contract, units, recommended range, and response fields
Newtons convert with the exact relation one kilogram-force equals 9.80665 newtons; pound-force converts with one lbf equals 0.45359237 kgf. Numerics are rounded to twelve decimal places for stable goldens. Worked example: three thousand kilogram-force on a ten millimetre ball with a 3.4 millimetre impression (d over D equals 0.34, F over D squared equals 30) yields about 320.583 HBW, depth about 0.298 millimetres, and area about 9.358 square millimetres. A five-hundred kilogram-force test on the same ten millimetre ball with d equals 4.2 millimetres is the F over D squared equals 5 condition and returns about 34.421 HBW. Readings outside the recommended window are still computed; the flag and message tell you the standard would not treat them as a valid official test. POST a JSON body with three required positive numbers: load (the applied Brinell force P; aliases F, force, P, applied_load, load_force), ball_diameter (the indenter diameter D; aliases D, indenter_diameter, ball, ball_d, indenter), and indent_diameter (the mean measured impression d; aliases d, impression_diameter, indentation, indentation_diameter, indent_d, impression). Optional load_unit is an enum of kgf (default), N, or lbf. Optional length_unit is an enum of mm (default) or in, and applies to both diameters; inches convert with one inch equals 25.4 millimetres. Fields may arrive as JSON numbers or numeric strings. Missing load, ball_diameter, or indent_diameter, a non-positive value, an unknown unit, or an impression that is not strictly smaller than the ball fail with invalid_input naming the problem; those failures are not billed. On success the body echoes the inputs and resolved units, returns load_kgf, ball_diameter_mm, and indent_diameter_mm, and then the derived indent_depth_mm, indent_area_mm2, load_diameter_ratio (P over D squared), nearest standard_fd2 among 1, 2.5, 5, 10, and 30, the ratio d_over_d, the boolean in_recommended_range for the 0.24 to 0.60 window, brinell_number, designation such as HBW 10/3000, unit HBW, formula, method brinell_astm_e10, and a short message.
Where a Brinell hardness number API earns its keep
Quality-system scripts can pin brinell_number and designation in continuous integration next to a coupon photograph. Keep requests small, pin the rounded brinell_number field in tests, and you get reproducible Brinell numbers for LMS plugins, edge workers, and shop-floor kiosks without standing up a metrology package or trusting a handheld tester’s undocumented firmware.
Integration use cases
Homework and materials-science labs
Check the ASTM E10 spherical-cap formula, including newton or inch inputs, against textbook problems with the same pure module as the free browser widget.
QA automation and LMS grading
Call a deterministic API to grade Brinell-number items or to pin HBW and the HBW D/P designation in production test scripts without a spreadsheet.
Technical questions
Why was my indentation rejected?
indent_diameter must be strictly smaller than ball_diameter; otherwise D² − d² is not positive and the spherical cap is undefined. Missing or non-positive load, D, or d, and unknown units, also fail with invalid_input and are not billed.
What does the Brinell hardness number calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.