# How do i calculate the square footage of a hip roof

**Question:** Unfortuantely the pictures do not show up, but here is how the math works.

The following drawing shows 3 views of a Hip Roof. TOP

With the information above we find the information needed to make each of the following: Ridge, Normal Rafters, End Rafters, Hip Rafters, and Jack Rafters. ( see the following figure ) We also find the squares of shingles and # sheets of plywood to cover the roof. length x width. It doesn’t matter if it’s a hip roof or not. length times width of all sections of it. add together. Unfortuantely the pictures do not show up, but here is how the math works.

The following drawing shows 3 views of a Hip Roof. TOP

With the information above we find the information needed to make each of the following: Ridge, Normal Rafters, End Rafters, Hip Rafters, and Jack Rafters. ( see the following figure ) We also find the squares of shingles and # sheets of plywood to cover the roof.

Derivation TOP

Following is the derivation of the formulas used, and drawings showing the what the various measurements indicate.

Axis TOP

The following figures show the axis and several useful points used in the following calculations. Point O is the origin of the axis, point T is the top of the hip rafter on the bottom-left side.

The pitch of a roof is normally given in the form: " pitch: 4 inch / (12 inch)". For calculations, We need the pitch as an angle so:

pitchAngle: atan( pitch );

All rafters are assumed to be made from 2 by X stock which has a thickness of ( 1 + 1/2 ) inch. If that is not the case you would change the following.

thickness: ( 1 + 1/2 ) inch;

Point T ( shown below ) is used in several calculations. Note: Point O is the origin which has the coordinates (0,0,0). With this choice of origin the coordinates of T are also the values for the vector T.

The coordinates for T are:

Ty: (sideR — thickness) / 2;

Tx: Ty;

Tz: Ty tan( pitchAngle );

T: Tx `i + Ty `j + Tz `k;

Ridge TOP

The length of the ridge is:

RidgeLength: sideF — 2 Tx;

Hip Rafters TOP

The following figure shows the front part of the roof looking normal ( perpendicular ) to the surface.

The length of all the hip rafters are the same and equal to the length of vector T. angle_1 is used to find the lengths of the jack rafters. ( See angle notes )

Next is a detailed view of a hip rafter, and the formula to find the HipAngle.

C: 0 m `i + 0 m `j + m `k;

HipAngle: acos( T dot C / ( abs( T ) abs( C ) ) );

The other cut for the Hip Rafter is 90 deg as shown below.

Plywood Cuts at the Hip Rafters TOP

Given angle_1 ( found above ), we can cut the plywood for the roof at the hip rafters, but angles are difficult to measure. It is easier to measure the length cut off as shown below.

The Next figure shows an overview of jack rafter.

The Next figure shows the same rafter in much more detail.

The length of a given jack rafter is found by first finding the x location, and then finding the length at that point. To simplify matters, you only need specify the # (JRN) of the jack rafter you are looking for. JRN 1 is the first rafter after the last full rafter, 2 is the next, etc. angle_1 was found in the hip rafter section.

RafterSpacing: 16 inch;

Gx: thickness cos( 45 deg );

jackLenght: ( Jackx — Gx ) tan( angle_1 );

The number of jack rafters on each side of the hip rafter assuming that we don’t want any closer than 1 foot from the hip rafter is:

numberOfJackRafters: ( Tx — ft ) / RafterSpacing — frac( ( Tx — ft ) / RafterSpacing );