For the 1:x ratio, enter and receive just the number x (for example, for "1:10" enter 10). The ratio shows how many horizontal length units correspond to one vertical rise unit.
Result
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Facts and limits of this method
| Percent → degrees formula | angle = arctan(percent / 100) |
|---|---|
| Degrees → percent formula | percent = tan(angle) × 100 |
| 45° slope | = 100% = ratio 1:1 |
| Degree range | 0° (flat) to nearly 90° (vertical) — excluding true vertical |
When it misleads you
- Slope percent and slope degrees are related nonlinearly through the tangent function — a 100% slope corresponds not to 90° but to exactly 45°; for slopes steeper than 100%, percent grows much faster than degrees.
- The 1:x ratio is conventionally written so the first number (usually 1) is the vertical rise and x is the horizontal run; the larger x is, the gentler the slope. The converter works with the number x itself, not the full "1:x" notation.
- As slope approaches vertical (90°), the percent grade approaches infinity while x in the 1:x ratio approaches zero — the converter won't produce a result for a perfectly vertical slope.
- Rounding is applied only to the displayed result — internal calculations use the full precision of JavaScript floating-point numbers.
How it is calculated
The entered value is first converted to degrees: percent via arctangent (angle = arctan(value/100)), a 1:x ratio also via arctangent (angle = arctan(1/x)).
If the "from" unit is already degrees, this step leaves the number unchanged.
The angle in degrees is then converted to the target unit using the inverse formula — to percent via tangent, to a 1:x ratio via cotangent (1/tan(angle)).
The result is rounded to the chosen number of decimal places and updates instantly whenever the value, units or precision change.
Questions and answers
What does a 100 percent slope mean?
100% means rising one meter (or any unit) vertically for every meter of horizontal distance — this corresponds to an angle of exactly 45°, not 90° as sometimes mistakenly assumed.
How do I read a "1:10 slope"?
It means 10 units of horizontal distance for every 1 unit of vertical rise — a fairly gentle slope, equivalent to 10% or about 5.7°.
Why does percent grow much faster than degrees on very steep slopes?
Because the relationship between them is the tangent of the angle, not a linear function: as the angle approaches 90°, the tangent — and so the slope percent — approaches infinity.
Is my data sent anywhere?
No, the whole calculation runs in your browser.