A snowman is three spheres, and spheres hold the most snow for the least surface – which is also why a round snowman melts more slowly than a square one. The size you can build depends on how much snow you have: a fluffy 20 cm of fresh powder weighs far less than the same depth of wet, heavy snow that is perfect for packing. Rolling compacts the snow into balls of roughly 400–500 kg per cubic metre, so a large snowman quickly gets surprisingly heavy.
Choose what you want to know. In the first mode, enter the snow depth, the snow type and the area you can clear and the calculator finds the largest snowman in the proportion you like – classic 2 : 3 : 4, Fibonacci 2 : 3 : 5, the golden ratio or 1 : 2 : 3. In the second mode, enter the size of the bottom ball (or every diameter) to find the snow and the area of garden it takes.
Every ball gets a weight, so you can judge whether one person can lift the middle ball onto the base. A simple degree-day melt model estimates how many days the snowman survives at the forecast temperature in shade or sun.
How to use the Snowman Calculator
- What do you want to know?
- Snow depth
- Snow type
- Area given as
- Snow-covered area you can use
- Length
- Width
- Radius
- Share of the snow you can roll up
- Density of the rolled balls
- Number of balls
- Ball size ratio
- Diameter of the bottom ball
- Diameter of ball 1
- Diameter of ball 2
- Diameter of ball 3
- Diameter of ball 4
- Air temperature in the coming days
- Where it stands
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The calculator turns the snow you can collect into mass, divides by the density of the rolled balls to get their total volume, and scales the chosen ratio so the three (or two or four) spheres use exactly that volume. Melting removes a layer of DDF × T millimetres of water a day from every ball.
Worked example
A 4 m² patch of settled snow (250 kg/m³) 15 cm deep holds 4 × 0.15 × 250 = 150 kg; rolling up 80% gives 120 kg. Packed to 450 kg/m³ that is 0.267 m³ of snowball. For the 2 : 3 : 4 ratio, Σk³ = 8 + 27 + 64 = 99, so the scale is ∛(6 × 0.267 ÷ (π × 99)) = 0.173 m and the balls are 34.5, 51.8 and 69.1 cm across. The snowman stands about 1.42 m tall; the balls weigh 9.7, 32.7 and 77.6 kg.
Snow density guide
| Snow | Density | Packs well? |
|---|---|---|
| Fresh powder | 50–100 kg/m³ | No |
| Fresh moist snow | 100–200 kg/m³ | Sometimes |
| Settled snow | 200–300 kg/m³ | Yes |
| Wet snow near 0 °C | 300–400 kg/m³ | Best |
| Old, refrozen snow | 400–550 kg/m³ | Hard to roll |
Formula
Snow mass = area × depth × snow density × usable share · Ball volume = πd³/6 · Diameters = k·s with s = ∛(6M ÷ (π ρ_ball Σk³)) · Height = Σd − 15% of each smaller ball · Melt rate ≈ DDF × T ÷ ρ_ball (degree-day model)
Worked example
Inputs — What do you want to know?: How big a snowman can my snow make?; Snow depth: 15 cm; Snow type: Settled snow – 250 kg/m³; Area given as: Area; Snow-covered area you can use: 4 m²; Share of the snow you can roll up: 80 %; Density of the rolled balls: Firmly packed – 450 kg/m³; Number of balls: 3 balls (classic); Ball size ratio: Classic 2 : 3 : 4; Air temperature in the coming days: 2 °C; Where it stands: Partly sunny.
Results — Height of the snowman = 1.42; Balls = Ball Diameter Weight
──────────────────────────────────────────────
Head 34.5 cm (13.6 in) 9.7 kg (21.4 lb)
Middle 51.8 cm (20.4 in) 32.7 kg (72.2 lb)
Base 69.1 cm (27.2 in) 77.6 kg (171 lb); Bottom ball diameter = 0.7; Total weight = 120; Are you strong enough? = Lifting the middle (32.7 kg) is a job for two people – or roll it up a snow ramp.; Survival time = The head is gone in about 7.8 days and the base in about 15.5 days at a steady 2 °C..
Key terms
- Snow density
- Mass of snow per cubic metre; fresh powder is 50–100 kg/m³, wet packed snow 300–500 kg/m³.
- Degree-day factor (DDF)
- Millimetres of water melted per degree above 0 °C per day, typically 3–8 mm.
- Golden ratio
- φ ≈ 1.618, the limit of the ratio between consecutive Fibonacci numbers.
Frequently asked questions
How much snow do I need for a snowman?
A 1.65 m snowman with 40, 60 and 80 cm balls weighs about 187 kg at 450 kg/m³. With 20 cm of settled snow and 80% usable, that takes about 4.7 m² of garden.
What is the best ratio for snowman balls?
2 : 3 : 4 looks classic; Fibonacci 2 : 3 : 5 and the golden ratio give a bigger, more stable base.
What is the best snow for a snowman?
Wet, sticky snow near 0 °C (32 °F) with a few per cent liquid water packs well. Dry powder below about −5 °C will not stick.
How heavy is a snowball 60 cm across?
About 51 kg when firmly packed at 450 kg/m³ – a job for two people.
How long does a snowman last?
Below freezing, weeks; at a steady 2 °C in partial sun a 35 cm head lasts about 8 days and a 70 cm base about 15 days in this model.
Why do snowmen melt from one side?
Sunshine adds energy on the sunny side, so the sun-facing side melts several times faster than the shaded side.