Angle to Pitch Calculator: Convert Degrees and Rise

An angle-to-pitch calculator converts a roof or ramp angle into pitch, expressed as rise per 12 units of horizontal run, and can also convert pitch back into an angle. Enter the angle in degrees or the rise and run in matching units; the calculator returns the equivalent pitch or angle.

Formula

For an angle θ measured up from the horizontal, pitch per 12 units of run is pitch = 12 × tan(θ). Slope percentage is slope = 100 × tan(θ). The calculator’s input a is the angle in degrees; pitch is the vertical rise for 12 units of horizontal run, and pct is the rise divided by horizontal run, expressed as a percentage. The degree-based function tand evaluates the tangent using degrees.

Pitch is a ratio, not an angle or a roof length. For example, a pitch of 6/12 means 6 units of vertical rise for every 12 units of horizontal run. The units can be inches, centimetres, feet, or metres, provided rise and run use the same unit. The ratio itself does not change when the units change.

Worked Example

Using the default angle of 30°:

1. Find the tangent: tan(30°) ≈ 0.577350.
2. Multiply by 12: pitch = 12 × 0.577350 ≈ 6.9282.
3. Round to two decimal places: pitch = 6.93 units of rise per 12 units of run.
4. Convert the same ratio to a percentage: 100 × 0.577350 ≈ 57.74%.

Thus, the calculator’s headline result is a pitch of 6.93 per 12, and its additional slope result is 57.74%. A practical roof notation might round the first value to about 6.9/12, but use the unrounded value for calculations that need precision.

What Angle and Pitch Mean

An angle describes a line’s direction relative to a reference line. In building work, roof angle is generally measured from horizontal. Pitch describes the same steepness as a rise-to-run ratio. Converting between them is useful because plans, calculators, measuring tools, and construction conventions may express slope in different ways.

A common source of confusion is that “pitch” can mean different things in different fields. For roof pitch, it often means rise per 12 units of horizontal run. In some engineering contexts, pitch simply means a ratio such as rise/run, without the 12-unit convention. Always check the convention before comparing values.

For a 30° angle, the rise/run ratio is about 0.57735. Multiplying by 12 gives 6.93/12. This does not mean the roof surface is 6.93 units long, nor that it rises 6.93 units over a 12-unit length measured along the slope. The 12 is horizontal run.

How to Convert Pitch Back to an Angle

If you know rise and run, calculate the angle with the inverse tangent: θ = arctan(rise ÷ run). If pitch is stated as P/12, then θ = arctan(P ÷ 12). Set the calculator or scientific calculator to degrees if you want a result such as 26.57°, rather than radians.

For example, a 6/12 pitch gives arctan(6 ÷ 12), or about 26.57°. Its slope percentage is 6 ÷ 12 × 100 = 50%. These three descriptions—6/12, 26.57°, and 50%—represent the same ideal straight slope.

Using the Result in Measurements

For a straight, symmetrical roof, the relevant run is the horizontal distance from the ridge’s vertical projection to the outside wall or other chosen eave reference. The rise is the vertical difference between those points. If you know the angle and horizontal run, the vertical rise is run × tan(angle). If you need the length along the sloping roof surface, use run ÷ cos(angle), assuming the angle is measured from horizontal.

• Keep rise and run in the same units: inches with inches, or centimetres with centimetres.
• Distinguish horizontal run from the sloped length of a rafter or ramp.
• State whether a percentage means rise divided by horizontal run. That is the usual slope definition.
• Keep extra decimal places during intermediate calculations, then round the final value to the precision your task requires.

On an existing structure, the measured surface may not be perfectly straight, and framing, finishes, or measurement points can affect the result. A calculator describes ideal geometry; it does not verify that a roof or ramp matches a plan.

Common Errors and Limitations

The tangent formula uses the angle from horizontal. If an angle is measured from vertical, convert it first: for an acute angle, its complement is 90° minus that angle. Entering a vertical-referenced angle as though it were horizontal can produce a very different pitch.

Another frequent error is treating a 6/12 pitch as 6 degrees or as a 6% slope. It is neither: 6/12 equals a 50% slope and an angle of about 26.57°. Likewise, the percentage is not the angle in degrees multiplied by 100.

The calculator’s angle input must be between 0° and, but not including, 90° for a finite positive rise per run. At 0°, the surface is level; as the angle approaches 90°, the horizontal run approaches zero and the calculated pitch grows without limit. Real projects also involve measurement tolerance, uneven surfaces, and design requirements that a simple trigonometric conversion cannot assess.

Frequently Asked Questions

How do I convert a roof angle to pitch?
Use pitch per 12 = 12 × tan(angle in degrees). For example, a 30° angle is about 6.93/12.

How do I convert a 6/12 pitch to degrees?
Calculate arctan(6 ÷ 12), with the calculator set to degrees. The result is approximately 26.57°.

Is roof pitch the same as slope percentage?
No. Pitch is commonly written as rise per 12 units of horizontal run, while slope percentage is rise divided by run multiplied by 100. A 6/12 pitch equals a 50% slope.

Does the unit matter when calculating pitch?
The ratio is unitless if rise and run use matching units. A rise of 6 inches over 12 inches gives the same pitch as 6 centimetres over 12 centimetres.

Is the roof angle measured from horizontal or vertical?
Roof slope angles are generally measured from horizontal. Confirm the reference used by your drawing or measuring tool before converting.

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in a | Angle | degrees | 30 | 0
out pitch | Pitch (rise per 12 run) | in/12 | 12 * tand(a) | 2
out pct | Slope | % | 100 * tand(a) | 2