Hydraulic radius calculator
A section with 2 m² of flow area and 4 m of wetted perimeter has a hydraulic radius of 0.5 m. Divide area by wetted length to get the characteristic length that Manning, Chezy or a Reynolds number needs. Free in your browser.
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Run — free
Worked example
- Area
- 2
- Wetted perimeter
- 4
- Hydraulic radius
- 0.5
- Radius
- 0.5
Hydraulic radius is the ratio of a channel's cross-sectional flow area to the length of the wetted perimeter — the textbook identity R = A / P used in open-channel hydraulics, Manning and Chezy resistance formulas, and pipe-flow Reynolds numbers. Given a finite flow area and a non-zero wetted perimeter in consistent length units, this calculator returns the hydraulic radius in the same length unit as the perimeter.
What hydraulic radius means and when R = A/P applies
Hydraulic radius is a characteristic length of a flowing section, not the geometric radius of a circle. It is defined as the cross-sectional flow area A divided by the wetted perimeter P, the length of the solid–fluid boundary in that section. A full circular pipe of diameter D has A = π D² / 4 and P = π D, so R = D / 4 — a result every hydraulics course asks students to recover.
Trapezoidal, triangular, and compound sections follow the same ratio once A and P are known from geometry. Search intent clusters around hydraulic radius calculator, R = A/P, wetted perimeter, Manning formula hydraulic radius, and open-channel characteristic length: people who already have area and wetted length and want a numeric R they can drop into Manning, Chezy, Darcy–Weisbach, or a Reynolds number, not a unit converter for soil conductivity and not a circle-radius tool. This landing computes that ratio only.
Keep units consistent: square metres with metres yield metres; square feet with feet yield feet.
Where hydraulic radius is used, nearby tools, and pricing
Open-channel designers use hydraulic radius as the length that multiplies the energy slope in the Manning and Chezy uniform-flow formulas: mean velocity is proportional to R to the two-thirds times the square root of slope, so a wrong R throws every discharge estimate. Culvert and sewer calculations often start from a full-pipe identity R = D/4 and then recompute A and P as the pipe runs part-full.
Teaching labs ask students to tabulate A, P, and R for a rectangular flume as depth changes, and to see that R is not the geometric radius and is not the hydraulic diameter. Field notes that already list a surveyed area and a tape of the wetted boundary can convert those two numbers into R without opening a full Saint-Venant solver.
This page is not a hydraulic-conductivity converter — that quantity is a soil or aquifer property with different units and a different search — and it is not a hoop-stress or pipe-flow-rate tool. Use the browser form when you want an immediate check while grading a homework set or comparing a hand calculation of A over P. Results are fully deterministic: identical inputs always produce the same hydraulic radius and the same formula and method labels, with no language model, no outbound network, and no wall-clock dependence.
What you can do with it
Manning and Chezy uniform-flow checks
Convert a surveyed or designed flow area and wetted perimeter into hydraulic radius R before evaluating Manning or Chezy velocity on a canal, culvert, or natural channel.
Hydraulics homework and lab keys
Generate deterministic R for rectangular, trapezoidal, and full-circular sections so students can check A/P against flume data without mixing geometric radius and hydraulic diameter.
FAQ
Why is a zero wetted perimeter rejected?
R = A/P is undefined when P is zero.
Which units should I use for hydraulic radius?
Any consistent length system. Square metres with metres yield R in metres; square feet with feet yield R in feet. The calculator does not convert units. Do not include the free surface in the wetted perimeter.
How is hydraulic radius different from hydraulic diameter or geometric radius?
Hydraulic radius is A/P. Hydraulic diameter is usually 4R and is used for non-circular closed conduits. Geometric radius is a circle's r. For a full circular pipe, R = D/4, which is not the pipe radius.
Does the water surface count in the wetted perimeter?
No. At the surface of an open channel the water touches air, not a bed or a wall. A rectangular canal therefore counts the width plus both side depths, never the top width.
What is the hydraulic radius of a full circular pipe?
It is a quarter of the diameter. The area of the full pipe divided by its whole circumference cancels down to the diameter over four, a result most hydraulics courses ask students to recover.
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/phys/hydraulic-radius \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"area":2,"wetted_perimeter":4}'const res = await fetch("https://api.kit.forhosting.com/phys/hydraulic-radius", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"area": 2,
"wetted_perimeter": 4
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/hydraulic-radius",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"area": 2,
"wetted_perimeter": 4
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/hydraulic-radius", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"area":2,"wetted_perimeter":4}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"area":2,"wetted_perimeter":4}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/hydraulic-radius", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"area": 2,
"wetted_perimeter": 4
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.hydraulic_radius",
"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_abs_area | 1000000000000 |
max_abs_wetted_perimeter | 1000000000000 |
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
A dry section with zero area yields R = 0; a zero wetted perimeter is physically and algebraically undefined and fails with invalid_input instead of a division-by-zero. Successful API calls are billed at $0.002; failed validation is not charged.
What hydraulic radius means and when R = A/P applies
The free surface of an open channel is not wetted perimeter: water there touches air, not a bed or a wall, so a rectangular canal of width b and flow depth y has A = b y and P = b + 2 y, hence R = b y / (b + 2 y), which approaches the depth y only when the channel is very wide. It does not derive A or P from a named shape, look up a roughness n, or convert hydraulic radius into hydraulic diameter D_h = 4 R, which is a related but distinct quantity used mainly for non-circular closed conduits.
How this calculator validates input and applies R = A/P
Area must be non-negative: a negative section is not a physical channel, while a zero area is a dry bed and returns hydraulic radius 0. Wetted perimeter must be strictly positive. A negative wetted length is likewise rejected. Magnitudes above one trillion are rejected as outside the supported range. There is no geometry helper, no unit conversion, and no roughness table; this is the pure ratio only. Send a JSON body with two required fields: area, the cross-sectional flow area A, and wetted_perimeter, the wetted length P. Every field must be a finite number or a numeric string that parses to one; missing fields, empty strings, bare plus or minus or a lone decimal point, non-numeric text, NaN, and Infinity all fail immediately with invalid_input naming the field, and failed validation is not billed. Optional aliases A, flow_area, cross_section, cross_section_area, and section_area are accepted for area; aliases P, perimeter, wetted, wp, and hydraulic_perimeter are accepted for wetted_perimeter so forms and scripts can use textbook symbols. After validation the engine divides area by wetted perimeter and rounds both inputs and the result to twelve decimal places so the same request always yields the same JSON across JavaScript engines. The body echoes area and wetted_perimeter, reports hydraulic_radius and the synonym radius as the same number, and labels formula R = A / P with method area_over_wetted_perimeter.
Where hydraulic radius is used, nearby tools, and pricing
Each successful request is one billable item at $0.002; failed validation does not consume balance.
Integration use cases
Open-channel software fixtures
Pin expected hydraulic radius in unit tests for SI and imperial units, including the full-pipe identity R = D/4, without embedding a full geometry library.
Technical questions
How do I calculate the hydraulic radius of a channel?
Hydraulic radius is flow area divided by wetted perimeter: R = A / P. Send those two finite numbers (area non-negative, wetted_perimeter strictly positive) and the API returns hydraulic_radius in the same length unit as P.
What does the hydraulic radius calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.