Slope grade converter
A 10% grade is a 1:10 rise over run and about 5.71 degrees, not 10. Enter one slope as a percent, an angle or a ratio and get the other two, for road plans, ramps and survey notes. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Slope magnitude to convert
- 10
- Output format
- percent
- Result
- 10
- Percent grade
- 10
- Degrees
- 5.7105931375
- Ratio
- 0.1
Slope grade conversion between percentage grade, degrees of inclination, and rise-over-run ratio is a daily task for civil engineers checking road and ramp designs, surveyors comparing field notes written on different scales, landscape architects sizing paths and retaining walls, wheelchair-access planners verifying ADA-style ramp limits, mountain-biking and ski-trail writers describing difficulty, and students translating textbook problems that mix percent grade with angle. People search for a slope grade converter when they need one slope figure restated on every common scale, not a general multi-category unit toolbox that also converts mass or temperature, and not an inclined-plane dynamics calculator that solves forces and acceleration. This capability accepts one finite value plus a format label among percent, degrees, and ratio, bridges every conversion through the dimensionless rise-over-run ratio so percent grade equals one hundred times the ratio and degrees equal the arctangent of the ratio in degrees, and returns the full triple of equivalent representations together with a compact rise-over-run label. Vertical slopes where the absolute value of the angle reaches ninety degrees are rejected because the rise-over-run ratio has no finite value on a vertical line. Unrecognized format names fail with a clear validation error instead of silently guessing a nearby symbol.
How the slope grade converter maps percent, degrees and rise-over-run through a ratio bridge
Start from the dimensionless rise-over-run ratio as the coherent intermediate: ratio equals vertical rise divided by horizontal run on a right triangle that models the slope. Percentage grade is one hundred times that ratio, so a ten percent grade means a ratio of zero point one, or one unit of rise for every ten units of run. Degrees of inclination are the arctangent of the same ratio converted from radians to degrees, so ten percent grade is about five point seven one degrees, not ten degrees.
Going the other way, a known angle in degrees produces ratio equals the tangent of the angle in radians, and percent grade is again one hundred times that ratio. A known percent grade divides by one hundred to recover the ratio, then the arctangent path recovers degrees.
This calculator never mixes those paths ad hoc: every conversion shares the same intermediate, so converting a six percent highway grade to degrees and back, or comparing a survey note in degrees with a road plan in percent grade, stays numerically consistent within ordinary floating-point precision. The vertical case is special and is rejected on purpose. Flat slopes are legal: zero percent, zero degrees, and ratio zero all map to each other cleanly.
Negative values are allowed and mean downhill or reverse grade on the same signed convention, so negative ten percent yields a negative ratio and a negative angle. The tool does not fetch elevation models, does not design structural members, does not estimate traction or vehicle gradeability, and does not solve inclined-plane force problems. It answers only the algebraic slope-grade unit conversion people mean when they type slope grade converter into a search bar and expect percent grade, degrees, and rise-over-run together.
What you enter and what you get back
Send two fields: value, a finite number for the slope magnitude on the chosen scale; and format, a string naming that scale. Both fields are required. For percent, value is the grade percentage itself, so ten means ten percent grade.
For degrees, value is the inclination angle in degrees and must satisfy absolute value strictly less than ninety. For ratio, value is the decimal rise divided by run, so zero point one means one over ten. When a format string is unknown the error message includes Unrecognized format and lists the three supported families so clients can fix the label rather than guessing.
When the input is degrees with absolute value at or above ninety the error explains that vertical slope is undefined because the rise-over-run ratio has no finite value. Classic checks include ten percent grade becoming ratio zero point one and about five point seven one degrees, a forty-five degree slope becoming one hundred percent grade and ratio one, and a one-to-twelve ramp ratio becoming about eight point three three percent grade.
Where dedicated slope grade conversion shows up in real work
Highway and municipal road design constantly restate design grades from percent tables used in standards into degrees for geometry packages, or the reverse when a survey crew delivers angles and the plan set expects percent grade. Ramp and accessibility work checks maximum slopes against code limits often written as rise over run or as a percent, while architects and inspectors may quote the same limit in degrees for field instruments. Landscape and drainage plans mix ratio notes with percent labels when sizing swales, paths, and retaining walls.
Ski resorts, mountain-bike trail maps, and outdoor media describe trail steepness on mixed scales depending on region and audience, so editors need a trusted oracle that matches the arctangent definition rather than treating percent and degrees as interchangeable. Secondary-school and college trigonometry or civil-tech courses assign problems that give a percent grade and ask for the angle, or give a rise and run and ask for percent, often mixing all three representations in one worksheet.
Data pipelines that ingest mixed CAD exports with percent, degree, and ratio tags can call this capability once per sample instead of reimplementing atan and tan in every service. If you later need inclined-plane force and acceleration, general multi-category unit conversion, or pure angle unit conversion between degrees and radians alone, treat those as separate search intents and landings rather than overloading this slope grade converter page.
What you can do with it
Road and ramp design tables
Restate percent design grades as degrees or rise-over-run so survey notes, CAD packages, and standards tables share one slope figure.
Accessibility and site plans
Convert ramp and path limits among percent, ratio, and degrees when codes and field instruments use different conventions.
Homework and trail documentation
Map student or media slope figures among percent grade, degrees, and rise-over-run without hand-written atan tables.
FAQ
What is the difference between percent grade and degrees?
Percent grade is one hundred times rise divided by run. Degrees are the arctangent of that same ratio. Ten percent grade is about 5.71°, not 10°.
What is rise-over-run ratio?
It is the dimensionless slope m = rise/run. A 1:10 grade has ratio 0.1, which is also 10% grade.
Why is a vertical slope rejected?
At ±90° the tangent diverges, so rise/run has no finite value.
What does it cost?
The browser tool is free and runs locally.
Can I enter a negative slope?
Yes. A negative value means a downhill or reverse grade, and it converts the same way on all three scales. A flat slope is also valid: 0% is 0 degrees and a ratio of zero.
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/conv/slope-grade \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"value":10,"format":"percent"}'const res = await fetch("https://api.kit.forhosting.com/conv/slope-grade", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"value": 10,
"format": "percent"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/conv/slope-grade",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"value": 10,
"format": "percent"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/conv/slope-grade", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"value":10,"format":"percent"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"value":10,"format":"percent"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/conv/slope-grade", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"value": 10,
"format": "percent"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "conv.slope_grade",
"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
How the slope grade converter maps percent, degrees and rise-over-run through a ratio bridge
When the absolute value of the input angle reaches or exceeds ninety degrees, the tangent diverges and the rise-over-run ratio has no finite value; the API returns invalid_input with a message that vertical slope is undefined rather than inventing infinity.
What you send and what you get back from the API and browser form
Format accepts short keys and everyday words in any common casing, including percent or percentage or percent_grade or grade or pct, degrees or degree or deg or angle or inclination, and ratio or rise_run or rise_over_run or gradient or slope. Missing fields, non-numeric value strings, NaN, Infinity, and unrecognized format labels fail with invalid_input and are not charged. On success the response echoes the cleaned value and normalized format key, a result field restating the input on its own scale, percent_grade, degrees, and ratio with twelve significant digits of stable precision, a compact rise_over_run string such as one colon ten style for common grades, the formula string, and method rise_run_bridge. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where dedicated slope grade conversion shows up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Technical questions
Which input formats are accepted?
percent (percentage grade), degrees (inclination angle), and ratio (decimal rise/run), plus common aliases such as grade, deg, angle, rise_over_run, and gradient.