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ROOFING

Roof Pitch Calculator.

Convert roof rise and run into pitch, angle and slope multiplier. Advanced mode can apply that multiplier to a horizontal roof footprint to estimate a simple sloped surface area.

Rise and run can use inches or centimetres; keep both in the same unit because the pitch ratio is dimensionless.

IMPERIAL + METRIC · LIVE CALCULATION
ROOF PITCH CALCULATOR — CALCULATE
Calculator mode
Calculated result: 6:12
YOUR RESULT6:12

26.6° roof angle with a 1.118 slope multiplier.

BASE BREAKDOWN
Pitch6:12
Angle26.6°
Surface multiplier1.118
Calculated in your browser
HOW IT WORKS

Formula and calculation method.

Pitch ratio = rise ÷ run. Angle = atan(rise ÷ run). Multiplier = √(1 + ratio²).

Rise and run must use the same dimension. The ratio is unit-independent. The slope multiplier converts horizontal plan area to sloped surface area for a simple roof plane.

WORKED EXAMPLES

See the material estimate in context.

6:12 roof

6 in rise over 12 in run

Result: 26.6° and multiplier about 1.118.

A 1,000 ft² horizontal roof footprint corresponds to about 1,118 ft² of simple sloped surface before waste.

USE IT CAREFULLY

Assumptions and common mistakes.

Assumptions

  • Rise and run describe the same roof plane.

Mistakes to avoid

  • Using rafter length as horizontal run.
  • Mixing dimensions from different roof sections.
EDGE CASES

Handle unusual projects explicitly.

Multiple pitches

Calculate each roof plane or pitch separately.

LIMITATIONS

What the estimate leaves out.

Pitch and footprint alone do not determine valleys, hips, dormers, overhangs or structural loading.

FAQ

Material planning questions.

What is 6:12 pitch?

It rises 6 units for each 12 horizontal units.

Can it estimate sloped area?

Yes. Advanced mode applies the calculated multiplier to the horizontal roof area you enter.

PRACTICAL GUIDE

Roof Pitch Calculator guide

Roof pitch describes the relationship between vertical rise and horizontal run. This calculator is useful when you have two measurements from one roof plane and need the familiar rise-per-12 notation, the equivalent angle, or the slope multiplier used for a simple surface-area estimate.

The important measurement is horizontal run, not the sloping rafter length. Rise and run can be measured in inches, centimetres, or another length unit as long as both use the same unit. Because the units cancel in rise ÷ run, a 6 cm rise over 12 cm run has the same pitch and angle as 6 inches over 12 inches.

FORMULA AND VARIABLES

How the calculation works.

Formularatio = rise ÷ run; X:12 pitch = ratio × 12; angle = atan(ratio); slope multiplier = √(1 + ratio²)
  • rise = vertical change over the measured roof plane
  • run = horizontal distance over that same plane, not rafter length
  • X:12 = equivalent rise for 12 units of horizontal run
  • slope multiplier = sloped length or simple sloped area divided by the corresponding horizontal run or plan area
WORKED EXAMPLE

Follow the numbers in context.

6 inches of rise over 12 inches of run

The ratio is 6 ÷ 12 = 0.5. Expressed per 12 units of run, that is 6:12. atan(0.5) is about 26.6°, and √(1 + 0.5²) is about 1.118. A simple 1,000 ft² horizontal plan area at one uniform 6:12 slope corresponds to about 1,118 ft² of sloped surface before overhangs, waste, openings, hips, valleys, or other geometry.

150 mm rise over 600 mm run

The ratio is 150 ÷ 600 = 0.25, equivalent to 3:12. The angle is about 14.0° and the slope multiplier about 1.031. Using millimetres rather than inches does not change those results because rise and run use the same unit.

WHAT THE RESULT TELLS YOU

Use the number for the question this tool answers.

The pitch, angle, and multiplier are three views of the same geometry. The pitch is convenient construction notation, the angle expresses inclination in degrees, and the multiplier tells you how much longer the slope is than its horizontal projection.

A multiplier of 1.118 means a simple sloped length is about 11.8% longer than its horizontal run. Applied to a matching simple plan area, it gives the corresponding sloped surface area before project-specific additions and deductions.

Use the result as a geometry check for estimating and communication, not as a structural, access-safety, or roofing-system approval.

More detail: inputs, assumptions, mistakes and edge cases
HOW TO USE IT

Build a dependable estimate.

  1. Measure vertical rise and horizontal run from the same roof plane. If you measure from inside an attic, keep the level truly horizontal.
  2. Use the same length unit for both measurements. Do not enter a sloping rafter length in the run field.
  3. Read X:12 as a normalized pitch: 6:12 means six units of vertical rise for every twelve units of horizontal run.
  4. Use the multiplier only for simple slope geometry. Split roofs with different pitches into separate planes and calculate each one independently.
  5. Check the actual roofing product instructions, structural design, drainage requirements, and local rules separately; pitch conversion does not establish suitability.
UNITS AND INPUTS

Keep measurements compatible.

Rise and run must use the same unit, but that unit can be imperial or metric because their ratio is dimensionless.

Degrees and percent grade are different representations. A 6:12 pitch has ratio 0.5, angle about 26.6°, and grade 50%; 50% grade does not mean 50 degrees.

The X:12 convention normalizes the ratio to a 12-unit horizontal run. It does not mean the roof was physically measured over exactly 12 inches.

ASSUMPTIONS AND LIMITATIONS

Know what the result includes.

Assumptions

  • Rise and run describe one straight, uniform roof plane.
  • The entered run is horizontal and the rise is vertical.
  • When the multiplier is applied to plan area, the plan area corresponds to the same uniformly sloped surface.

Limitations

  • Pitch alone does not determine rafter size, structural capacity, snow or wind loading, fastening, drainage design, or whether a particular roof covering is permitted.
  • A footprint multiplied by one slope factor does not capture hips, valleys, dormers, overhangs, parapets, openings, curved sections, or multiple pitches.
  • Measurement error matters: a small error in rise or run changes the angle and multiplier, especially when the measured run is short.
COMMON MISTAKES

Avoid preventable errors.

  • Using the rafter or roof-surface length as run. Run is the horizontal leg of the right triangle.
  • Mixing units, such as entering rise in inches and run in centimetres, which produces a meaningless ratio.
  • Treating degrees, percent grade, and X:12 pitch as interchangeable numbers. They describe the same slope with different mathematics.
  • Multiplying an entire complex-roof footprint by one factor when different planes have different pitches or geometry.
  • Assuming a calculated pitch proves a roofing product is suitable. Minimum slopes and installation details come from current product and code requirements.
EDGE CASES

Check unusual inputs carefully.

A zero run has no finite rise/run ratio and cannot be converted with this method.

A zero rise represents a 0:12 horizontal plane with a 0° angle and multiplier 1, but waterproofing and drainage requirements are separate design questions.

For a roof with two or more pitches, calculate each plane separately and combine surface areas only after each plane has the correct multiplier.

If an existing roof sags or varies along its length, one short measurement may not represent the whole plane; take measurements appropriate to the work being planned.

FAQ

Questions about this calculation.

What does a 6:12 roof pitch mean?

It means the roof rises 6 units vertically for every 12 units of horizontal run. Its angle is about 26.6°.

Is roof run the same as rafter length?

No. Run is horizontal distance. The rafter follows the slope and is longer whenever rise is greater than zero.

Can I use centimetres or millimetres?

Yes. Use the same unit for both rise and run; the ratio, angle, and multiplier are unchanged by the chosen length unit.

Is a 50% slope the same as 50 degrees?

No. Percent grade is rise ÷ run × 100. A 50% grade corresponds to a 0.5 ratio, a 6:12 pitch, and an angle of about 26.6°.

What does the slope multiplier do?

For a simple uniform plane, it converts horizontal run to sloped length and a matching horizontal plan area to sloped surface area.

Can this tell me whether shingles or another roof covering are allowed?

No. Confirm minimum slope, underlayment, fastening, drainage, and other installation requirements from the current product documentation and applicable local rules.

RELATED TOOLS AND GUIDES

Continue the calculation.

Roofing Material CalculatorEstimate roofing quantities after establishing the relevant roof geometry.Square Footage CalculatorCheck rectangular plan areas before applying a slope multiplier.Construction materials estimatingReview measurement, waste, and ordering practices before buying materials.
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