Hip Roof Material & Angle Calculator

Calculate hip roof area, rafter lengths, and required materials including shingles and plywood. Features dynamic SVG visualization and pitch calculations.

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About

Constructing a hip roof where all sides slope downwards to the walls is structurally superior to a gable roof in high-wind areas, but significantly more complex to estimate. The geometry involves calculating not just the common rafter lengths, but also the hip rafters (which run diagonally at the corners) and the ridge board length. A miscalculation here doesn't just mean wasted lumber; it can compromise the structural integrity of the roof framing.

This calculator solves the geometric challenges of hip roof construction. By inputting your building's footprint and the desired roof pitch, it computes the exact surface area, rafter lengths, and framing angles. It further translates this geometry into a material list, estimating the number of plywood sheets for decking and bundles of shingles required, factoring in standard construction waste.

roofing calculator hip roof rafter length shingles calculator

Formulas

The calculation of a hip roof relies on the Pythagorean theorem extended into three dimensions. The Common Rafter length is the hypotenuse of the run and rise:

Lcommon = √run2 + rise2

The Hip Rafter connects the corner of the building to the ridge. Its run is the hypotenuse of a square formed by the building corners (run × √2 for equal pitch):

Lhip = √Lcommon2 + run2

Total Roof Area approximation for estimation:

Area = FloorArea × Multiplierpitch

Reference Data

Pitch (Rise/12)Angle (°)Multiplier (Common)Multiplier (Hip/Val)Valley Angle
1/124.76°1.00351.4167175.2°
2/129.46°1.01381.4240170.5°
3/1214.04°1.03081.4362166.0°
4/1218.43°1.05411.4530161.6°
5/1222.62°1.08331.4743157.4°
6/1226.57°1.11801.5000153.4°
7/1230.26°1.15771.5298149.6°
8/1233.69°1.20191.5635146.3°
9/1236.87°1.25001.6008143.1°
10/1239.81°1.30171.6415140.2°
11/1242.51°1.35661.6853137.5°
12/1245.00°1.41421.7321135.0°

Frequently Asked Questions

The common rafter runs perpendicular from the wall plate to the ridge. The hip rafter runs diagonally from the building corner to the ridge. Since it traverses the diagonal distance of the corner, it must be longer to reach the same height (ridge), and it also has a shallower pitch angle relative to the ground than the common rafters.
Yes, overhangs significantly increase the surface area and material requirements. You can specify the overhang length, which is added to the run of the rafters when calculating the total roof surface area for sheathing and shingles.
Hip roofs typically require a higher waste factor than gable roofs because of the diagonal cuts required at the hips and valleys. A standard waste factor is 10-15%, but complex roofs may require up to 20%. This calculator includes a selectable waste percentage field.
On a standard rectangular hip roof with equal pitches on all sides, the ridge length is equal to the Building Length minus the Building Width. If the building is square, the ridge length is zero, resulting in a pyramid roof.