A-frame tarp geometry: what ridge height really buys you

An A-frame pitch hangs the tarp over a ridgeline and pulls both long edges down to the ground. Three measurements decide its shape: the tarp's width across the ridge (W), its length along the ridge (L) and the height of the ridge above the ground (h). Floor width, wall angle, headroom and volume all follow from those three numbers and one right-angled triangle.

Three measurements set the shape

Look at the pitch from an open end. Each side of the tarp runs from the ridge down to the ground, and that sloping edge is half the tarp width, W/2. The ridge height is one short side of a right-angled triangle; half the floor is the other. Pythagoras gives the floor, and the sine of the wall angle is the ratio of height to slope:

half floor  = √((W/2)² − h²)
floor width = 2 × √((W/2)² − h²)
wall angle  = asin(h ÷ (W/2))     measured from the ground

The wall angle depends only on the ratio of ridge height to half the width. A 3 m tarp at 1.05 m and a 4 m tarp at 1.4 m both have walls at 44.4°, because 1.05 ÷ 1.5 and 1.4 ÷ 2 are both 0.7. Scale the tarp and the ridge together and the shape stays the same.

These are the equations the Shelter studio uses. The full set, including the line allowance, is on the methodology page.

Floor width and wall angle at different ridge heights

Raising the ridge trades floor width for height, and the trade gets steeper as the ridge rises. On a 3 m wide tarp, going from 0.6 m to 0.8 m costs 21 cm of floor. Going from 1.2 m to 1.4 m costs 72 cm, 40% of the floor that was left.

A 1.5 m ridge on a 3 m tarp is the hard limit: each side hangs vertically and the floor disappears. Long before that, the walls become so steep that most of the fabric is spent on height nobody can use while lying down.

Where the enclosed volume peaks

The end-on cross-section is a triangle whose area is half the floor multiplied by the ridge height. Multiply that by the length along the ridge and you have the volume under the tarp. For a fixed width, the cross-section is largest when the walls sit at 45°, which happens at h = W ÷ (2 × √2).

For a 3 m tarp that height is 1.06 m. The Shelter studio takes heights in 5 cm steps, so 1.05 m is the nearest setting: 1.12 m² of cross-section and 3.37 m³ under a 3 m length. Volume changes slowly near the peak. Dropping the ridge to 0.8 m loses only about a tenth of the cross-section, while lowering the fabric by 25 cm, which matters when the wind picks up.

half floor  = √(1.5² − 1.05²) = √1.1475 = 1.071 m
floor width = 2 × 1.071 = 2.14 m
wall angle  = asin(1.05 ÷ 1.5) = 44.4°
volume      = 1.071 × 1.05 × 3 = 3.37 m³
end guy     = √(1.05² + 1.5²) = 1.83 m each

Headroom is a strip of floor, not a single number

The ridge height only exists on the centre line. A point x metres to the side of the centre has less fabric above it:

clearance at x = h × (1 − x ÷ half floor)
strip with clearance c = floor width × (1 − c ÷ h)

The second line answers the practical question: how wide is the strip of floor that keeps at least a chosen clearance overhead? The table uses c = 50 cm. That figure is only an example; choose your own by measuring the bulkiest thing that has to fit, such as a lofted sleeping bag or someone sitting on a pad.

On a 3 m tarp the 50 cm strip is widest, about 1.12 m, with the ridge between 1.0 m and 1.05 m. At 0.8 m it narrows to 0.95 m, and at 0.6 m it is less than half a metre. Two 0.5 m sleeping pads laid side by side on the centre line take up 1 m of that strip, so near 1 m of ridge height both stay under at least 50 cm of fabric in the ideal model. Pads moved out towards the walls do not.

What a longer or wider tarp changes

Length along the ridge multiplies floor area and volume in proportion and changes nothing else. A 3 × 4 m tarp hung with the 4 m side along the ridge has the same 2.24 m floor and 41.8° walls at a 1 m ridge as a 3 × 3 m tarp, with a third more floor area. The extra length also puts more fabric between the sleeping area and the open ends, which is where wind-driven rain gets in. The 3×3 vs 3×4 m comparison sets out those figures, and what size tarp to choose works through other common sizes.

Width across the ridge is what buys floor width and headroom together. Hang the same 3 × 4 m tarp the other way, with 4 m across the ridge, and a 1.2 m ridge gives a 3.2 m floor with 36.9° walls, but only 3 m of length along the ridge. The space is wider and shorter. Whether that suits depends on whether people will sleep lengthwise under it or mostly sit.

A wider tarp or a higher ridge also needs longer lines to reach the stakes. How much guyline a tarp needs works through the ridgeline, end guys and tie-outs, and choosing guyline cord covers what that line is made of.

What the ideal triangle leaves out

The equations assume a flat sheet over a straight ridge, equal slopes and both edges staked at ground level. Real pitches depart from that in predictable ways.

• Fabric sags between the ridge and the stakes. Sag pulls the walls inside the ideal triangle and narrows the strip of usable clearance.
• Edges are often staked a little above the ground for airflow. That changes the triangle and leaves a gap where wind and rain can reach the floor.
• Sloping or uneven ground changes the floor under each wall differently.
• Doors, beaks, catenary cuts and mid-panel tie-outs reshape the ends and the walls.

None of these numbers describe wind loading, stake holding, condensation or how many people a tarp suits. Those depend on the ground, the weather and the equipment. For the weather side, see pitching a tarp for wind and rain. For the spot itself, choosing a campsite covers ground, water distance and overhead hazards, and sunrise bearing shows where the morning light will reach an open end.