CalcLibrary

Roof Pitch Calculator

Plan a roof side profile from rise and run, roof angle and run, or x:12 pitch and run. Get the matching roof angle, slope percent, roof ratio, and rafter lengths before you cut stock or compare roof options.

Units
Active roof equation
m
m
m
Examples

A gentle porch roof with a modest rise and a short overhang, useful for checking how much rafter stock the shallow slope actually needs.

Pitch (x:12)
1.8:12
Roof Angle
8.5 °
Slope Percent
15 %
Rise : Run Ratio
1:6.667
Wall-Line Rafter Length
2.43 m
Total Rafter Length
2.73 m

The overhang is converted into a sloped tail at the same roof angle before it is added to the total rafter length.

Geometry estimate only — use this to understand roof shape and rafter length, not as structural engineering, code approval, or span certification.

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Examples

How It Works

Formula

m=RNm = \frac{R}{N}

θ=arctan⁡(RN)\theta = \arctan\left(\frac{R}{N}\right)

P12=12⋅RNP_{12} = 12 \cdot \frac{R}{N}

L=R2+N2L = \sqrt{R^2 + N^2}

Ltotal=L+O⋅1+(RN)2L_{\mathrm{total}} = L + O \cdot \sqrt{1 + \left(\frac{R}{N}\right)^2}

Variables

RR

Rise of the roof profile(m or ft)

NN

Run of the roof profile(m or ft)

mm

Slope as rise divided by run

θ\theta

Roof angle above horizontal(°)

P12P_{12}

Rise in an x:12 roof pitch

LL

Wall-line rafter length(m or ft)

OO

Horizontal overhang projection(m or ft)

LtotalL_{\mathrm{total}}

Total rafter length including overhang tail(m or ft)

Choose the mode that matches what you know: measured rise and run, a roof angle and run, or an x:12 pitch and run. The calculator resolves the same right-triangle roof profile in every mode, then reports the matching pitch, angle, slope percent, wall-line rafter length, and total rafter length with any overhang tail carried along the same slope.

Frequently Asked Questions

01What does x:12 roof pitch mean?
An x:12 pitch states how much the roof rises for every 12 horizontal units of run. A 6:12 roof rises 6 units for each 12 units of run, which is the same geometry no matter which measurement unit you use.
02What is the difference between wall-line rafter length and total rafter length?
Wall-line rafter length covers the main right triangle from the wall line to the high point. Total rafter length adds the overhang tail along the same slope so you can estimate a fuller stock length.
03How is overhang handled here?
The overhang input is treated as a horizontal projection beyond the wall line. The calculator then converts that projection into extra sloped tail length before adding it to the total rafter length.
04Will the three input modes agree on the same roof?
Yes. Rise + run, angle + run, and pitch + run all resolve to the same roof geometry when they describe the same slope. The calculator simply starts from a different known input and derives the rest.
05Is this a structural or code-compliance check?
No. This is a geometry estimator for roof shape, slope, and rafter length. It does not judge spans, loads, fastening, material suitability, or code approval.

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