Ice Bath Fill Level Calculator: How Full Before You Get In

Fill a plunge tub to the brim and the first person in floods the deck; fill it too low and the water stops at your chest. The fix is simple physics. Your body is close to the density of water, so every kilo of you that goes under pushes roughly one litre of water up the sides. Tell the calculator the tub's inside size, who is getting in and how deep you sit, and it gives you the line to fill to before anyone climbs in.

How the fill line is worked out

The tub's floor area sets how many litres fill each centimetre of depth: length times width for a rectangle, pi times the radius squared for a round tub, and pi times half the length times half the width for an oval. Divide that area in square centimetres by 1,000 and you have litres per centimetre.

When you sit in, the part of you under the water pushes aside its own volume. A human body averages close to the density of water, so the calculator takes one litre per kilo of the submerged part. How much of you is submerged comes from the body-segment tables used in biomechanics, where the head and neck make up roughly 8% of body mass and the legs and pelvis a little under half. That gives about 92% of your weight under water to the neck, 65% to mid-chest and 48% to the waist. Divide the litres you displace by the litres per centimetre and you have the rise. Take the rise and your chosen gap off the tub's inside depth, and what is left is the depth to fill to.

Ice floats, but a floating object still displaces its own weight of water, so each kilo of ice raises the level by about a litre's worth straight away. When it melts it turns into almost exactly that litre, so the level barely moves as it goes. The calculator counts it once.

Worked example: a round tub 90 cm across and 80 cm deep holds about 6.4 litres per centimetre. An 80 kg person sitting to the neck displaces about 74 litres, a rise of 11.6 cm. Leave an 8 cm gap and you fill to 80 minus 8 minus 11.6, which is about 60 cm, or roughly 384 litres.

Getting it right in practice

• Measure inside, not outside. Insulated tubs and barrels can have walls several centimetres thick, and the outside size will make the answer too generous.
• Leave a bigger gap than you think. Climbing in makes a wave, and two people moving about make a bigger one. Around 8 to 10 cm below the rim is a comfortable starting point; drop it to 5 cm once you know how your tub behaves.
• Tapered tubs need a check. If the tub narrows towards the floor, enter the inside size measured near the top, where the water line will sit, since that is what sets how far the level rises. The fill depth will be close, but the litres figure will read a little high. Test the line the first time with a bucket to hand.
• Mark the line. A strip of waterproof tape inside the wall at the fill depth saves measuring every time you top up after evaporation or splash losses.
• Mind the chiller connections. If you run a chiller or filter, check its inlet and outlet sit below your fill line, or it may draw air.

Once you know how many litres you fill to, the same figure drives the rest of your set-up: our ice calculator tells you how many bags to buy, the chlorine calculator doses the water, and the chiller size calculator matches a chiller to the volume.