Snowman Calculator (how big a snowman can you build from your snow?)

Understanding the snowman calculator — concept and principle

This calculator works out how big a snowman you can build from the snow on a patch of ground: the diameters of the bottom, middle and head balls, the total height and how heavy the bottom ball will be. It is a fun winter science project for families and classrooms.

Snow on the ground to balls: with the default inputs the result is 71 cm base ball (snowman 159 cm tall).

How it is calculated

Snow mass = depth × area × fresh-snow density.
Packed volume = mass ÷ packed-snow density.
Balls are spheres in fixed proportions k (for example 1 : 0.75 : 0.5): packed volume = π/6 × D³ × (1 + k₂³ + k₃³).
Bottom diameter D = ∛(6V ÷ (π × Σk³)); other balls = D × k.
Height = sum of diameters; bottom ball mass = total mass ÷ Σk³.

The principle

Snow is mostly air. Fresh snow often weighs around 100 kg/m³, while rolling a snowball packs it to several hundred kg/m³, so the snow you gather shrinks a lot in volume. A sphere's volume grows with the cube of its diameter, which is why the smaller balls take surprisingly little snow: a head half the bottom's diameter has only one eighth of its volume. Solving the sphere-volume formula backwards gives the bottom diameter from the packed volume.

Worked example

Default inputs: snow 10 cm deep over 10 m², fresh density 100 kg/m³, packed 350 kg/m³, balls 100% / 75% / 50%.

Snow mass = 0.10 × 10 × 100 = 100 kg.
Packed volume = 100 ÷ 350 = 0.286 m³.
Σk³ = 1 + 0.422 + 0.125 = 1.547; D = ∛(6 × 0.2857 ÷ (π × 1.547)) = 0.707 m = 71 cm.
Middle = 71 × 0.75 = 53 cm; head = 71 × 0.5 = 35 cm; height = 159 cm.
Bottom ball mass = 100 ÷ 1.547 = 65 kg.

Each point is the calculator re-run with only “Snow depth (cm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Snow depth (cm)	Bottom ball diameter (cm)
2.5	45
5	56
7.5	64
10	71
12.5	76
15	81
20	89

How to read the result

Real snowmen are a little shorter because each ball sinks into the one below. Wet, sticky snow near 0 °C packs best; very cold powder will not stick. The bottom ball is heavy, so roll it into its final place rather than lifting it.

Common mistakes

Using the fresh-snow depth after it has been trampled or blown away.
Expecting dry powder snow to pack.
Lifting a heavy ball instead of rolling it.
Gathering snow near roads, where it may be dirty or salty.

Keep in mind: Snow densities vary widely; treat the size as an estimate. Take care lifting heavy snow and keep away from roads and roof edges where snow may fall.

Frequently asked questions

How much snow do I need for a snowman?

About 100 kg of fresh snow makes a snowman about 1.6 m tall with 1 : 0.75 : 0.5 balls.

How heavy is a big snowball?

A 71 cm packed snowball weighs about 65 kg.

Why does wet snow work better?

Snow near 0 °C has liquid water that helps grains stick together when packed.

Sources: University of British Columbia, ATSC 113, "Newly-fallen snow density" (after R. Stull)

Checked 9 Nov 2026. University of British Columbia, ATSC 113 “Newly-fallen snow density” (after R. Stull): new snow generally 30–300 kg/m³, average about 80–110 kg/m³, newly compacted snow around 350 kg/m³; sphere volume π·d³/6. Ball proportions are example values.

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