Percent reduction of area calculator
Measure how much a tensile bar necked before it broke: an original area of 100 that shrinks to 60 at the fracture gives a reduction of area of 40 %. Use any area unit, as long as both match. Free in your browser.
- Free
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- No sign-up
- Your data stays on your device
Run — free
Worked example
- Original area
- 100
- Fractured area
- 60
- Area change
- 40 percent
- Reduction of area
- 0.4
- Reduction of area percent
- 40
Percent reduction of area is the tensile-test ductility measure that compares a specimen's original cross-section with the smallest section left at the fracture. Subtract the fractured area from the original area, divide by the original area, and multiply by one hundred: RA percent equals ((A0 minus Af) over A0) times 100. A large percentage means the bar necked a great deal before it broke, which is the signature of a ductile metal; a value near zero means the bar snapped with almost no necking and is comparatively brittle. This calculator takes the two areas in any consistent unit—square millimetres, square inches, or square metres—rejects a zero or negative original area because the formula would divide by zero, and returns the percent together with the area change and the unitless ratio.
What percent reduction of area means in a tensile test
When a standard tensile coupon is pulled to fracture, the load-bearing section does not stay the same size. After the onset of necking the local diameter or thickness collapses, so the area at the break is smaller than the original machined or as-received area. Percent reduction of area captures that collapse as a single ductility number.
With original area A0 and minimum fractured area Af, the definition used in ASTM E8 and ISO 6892 is RA percent equals ((A0 minus Af) divided by A0) times one hundred. The quantity is complementary to percent elongation: elongation tracks how much the gauge length grew, while reduction of area tracks how much the cross-section shrank at the neck. High RA—often fifty percent or more for annealed copper, mild steel, or many aluminium alloys—means extensive plastic flow before rupture.
Low RA—a few percent or less for grey cast iron, some high-strength steels, and most ceramics—means a brittle break with little necking. For a circular bar the areas are π d squared over four, so the same definition becomes one minus (df over d0) squared, times one hundred; this page still wants the areas themselves, so convert diameters first if that is what you measured. Units cancel: millimetres squared over millimetres squared is the same ratio as square inches over square inches, provided both fields share one unit.
Zero change (Af equals A0) is a legal brittle limit and returns zero percent, not an error. A zero original area is not legal, because the formula would divide by zero. This landing answers only that tensile RA% from two areas; it does not compute elongation, true strain, or a stress–strain curve.
Where reduction of area is used, priced, and kept distinct from elongation
Materials laboratories record RA% next to ultimate tensile strength and percent elongation on every certified tensile report, because a heat that meets strength but fails ductility is still out of specification. Quality engineers compare lot-to-lot RA on incoming bar, plate, or fastener stock before releasing a shipment. Students and graders need a deterministic oracle for homework that asks for reduction of area from two measured sections, without mixing the answer with elongation computed from gauge marks.
Teaching platforms and contest checkers call the same contract from scripts so a swapped pair (Af larger than A0) is rejected instead of silently producing a negative percent that a buggy grader might accept. Convert diameters to areas yourself if that is what the micrometer gave you, keep both fields in one unit, and you get a machine-readable RA% that matches the definition used in standard tensile testing.
What you can do with it
Tensile lab reports and coupons
Compute RA% from original and fractured cross-sections after a pull-to-fracture test and record it next to strength and elongation.
Incoming-stock ductility checks
Compare lot-to-lot reduction of area on bar, plate, or fasteners so a heat that meets strength but fails ductility is flagged.
Homework and automated grading
Score student RA% answers with a deterministic oracle that rejects a zero original area and a swapped Af greater than A0.
FAQ
How is percent reduction of area calculated?
RA (%) = ((A0 − Af) / A0) × 100, where A0 is the original cross-sectional area and Af is the minimum area at the fracture. Send both as finite numbers in the same unit.
What happens if the original area is zero?
Percent reduction of area is undefined when A0 is zero because the formula would divide by zero. Failed validation is not charged.
Can the fractured area be larger than the original area?
No. For a tensile specimen Af must be less than or equal to A0.
What units should I use for the areas?
Any consistent area unit—mm², in², or m². Units cancel in the ratio. If you measured diameters, convert first with A = πd²/4 and then send the areas.
I measured diameters, not areas. What should I do?
Convert each diameter to an area first: pi times the diameter squared, divided by four. For a round bar this is the same as one minus the squared ratio of final to original diameter, times 100.
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/reduction-of-area \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"original_area":100,"fractured_area":60}'const res = await fetch("https://api.kit.forhosting.com/eng/reduction-of-area", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"original_area": 100,
"fractured_area": 60
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/eng/reduction-of-area",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"original_area": 100,
"fractured_area": 60
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/eng/reduction-of-area", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"original_area":100,"fractured_area":60}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"original_area":100,"fractured_area":60}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/eng/reduction-of-area", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"original_area": 100,
"fractured_area": 60
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "eng.reduction_of_area",
"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
Successful API calls are billed at $0.002; invalid input is not charged.
How this calculator reads areas and what the response contains
Numeric strings that parse as finite decimals are accepted so forms and CSV-style pipelines can pass values without an extra cast. Original area must be strictly greater than zero: a zero or negative A0 is rejected because RA equals ((A0 minus Af) over A0) times one hundred is undefined when the original cross-section vanishes. Fractured area must be non-negative, and it must not exceed the original area: Af greater than A0 is not a reduction for a tensile fracture and usually means the two fields were swapped. There is no diameter mode, no unit conversion, and no material look-up; this is the pure two-area evaluation only. Send a JSON body with two required finite numbers: original_area for A0 and fractured_area for Af. Every field must be finite; missing fields, empty strings, non-numeric text, NaN, and Infinity fail immediately with invalid_input before any result is returned, and failed validation is not charged. Aliases are supported: A0, a0, A_0, Ao, original, and area_original for the original section; Af, af, A_f, final_area, fracture_area, area_fractured, and broken_area for the fracture section. After validation the engine subtracts Af from A0, divides by A0, multiplies by one hundred, and rounds to a stable twelve-significant-digit precision so identical inputs always produce the same JSON. The body echoes original_area and fractured_area, reports area_change as A0 minus Af, reports reduction_of_area as the unitless ratio between zero and one, reports reduction_of_area_percent as that ratio times one hundred, and labels unit as percent, formula as RA (%) equals ((A0 − Af) / A0) × 100, and method as tensile_reduction_of_area. Example: original_area one hundred and fractured_area sixty yields area_change forty, ratio zero point four, and forty percent RA.
Where reduction of area is used, priced, and kept distinct from elongation
Each successful request is one billable item at $0.002; failed validation does not consume balance.
Technical questions
What does the percent reduction of area calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.