How this calculator works
Each ball of a snowman is a sphere, and the volume of a sphere is pi divided by six times the cube of its diameter. With a chosen ratio of diameters, the total height fixes every diameter, so the total volume and mass follow from the snow density. Building in reverse is a cube root: the snow on the ground gives a fixed volume, and the largest snowman that fits uses all of it, so its height is the cube root of that volume divided by a shape factor. The shape factor depends only on the proportions of the balls, which is why a 1:2:3 snowman and a 3:5:8 snowman of the same height use different amounts of snow. Real snow also compacts, and rolling a ball leaves some behind.
Formula
diameter of ball i = height x ratio i / sum of ratios. volume of one ball = pi x diameter^3 / 6. total volume = sum of ball volumes. mass = volume x snow density. For a build, height = cube root of (available snow volume / shape factor), where shape factor = pi/6 x sum of ratio^3 / (sum of ratios)^3. Ground area needed = volume / depth.
Worked example
A three-ball snowman 1.5 metres tall with diameters in the ratio 1:2:3 has balls of 0.25, 0.5 and 0.75 metres. Their volumes add to pi/6 x (0.015625 + 0.125 + 0.421875) = 0.2945 cubic metres, which weighs 32.40 kilograms in damp snow at 110 kilograms per cubic metre. At a depth of 20 centimetres it needs 0.2945 / 0.2 = 1.47 square metres of ground. Going the other way, 2 cubic metres of damp snow can build a snowman 2.84 metres tall, weighing 220 kilograms.
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Frequently asked questions
How dense is snow?
Fresh powder is around 60 kilograms per cubic metre, damp snow that packs into balls is around 110, and settled or wet snow can reach 250 or more. The value you choose changes the mass a lot but not the volume.
Why does the calculator use spheres?
Rolled snow balls are close to spheres, and the volume formula is simple and accurate enough for planning. A real snowman is slightly flattened where the balls meet and where the base sits on the ground.
Can I build the snowman from the snow I have?
The build mode assumes you use all the snow and get every bit of it into the balls. Rolling loses some snow and the ground layer is not always usable, so leave a margin of 20 to 30 percent.
Does the ball ratio matter?
Yes. A 3:5:8 stack puts more volume in the base and less in the head for the same height, so it needs more snow and stands more stably. A 1:2:3 stack is the classic look.