Calculate single-phase thermal expansion, water-to-ice volume, or unconfined freezer headspace from volume, temperature change, density assumptions and freeze percentage. Headspace estimates do not predict pressure, container strength or safe fill levels.

Constant volumetric coefficient approximation within one phase; no freezing. Use a suitable coefficient for a small temperature interval.

Headspace is an unconfined volume estimate. It does not predict pressure, container strength or safe fill levels. Sealed containers can rupture during freezing.

Temperature difference; no 32-degree offset.

Coefficient examples

Related Calculators

Water-to-Ice Volume Expansion Formula

The following formula is used to calculate the volume after liquid water freezes into ice (phase-change expansion), using the densities of water and ice (mass is conserved).

Vice = Vwater ร— (ฯwater) / (ฯice)

Variables:

  • Vice is the ice volume after freezing
  • Vwater is the initial liquid-water volume
  • ฯwater is the density of liquid water (at the relevant temperature/pressure)
  • ฯice is the density of ice (at the relevant temperature/pressure)

Near 0ยฐC at 1 atm, a common approximation is ฯwater โ‰ˆ 999.84 kg/mยณ and ฯice โ‰ˆ 916.7 kg/mยณ, giving Vice/Vwater โ‰ˆ 1.0907 (about a 9.1% increase). For temperature-driven expansion/contraction without freezing, use the Thermal solve modes (ฮฑยทฮ”T).

What is Frozen Water Expansion?

Frozen water expansion refers to the increase in volume that occurs when water freezes and turns into ice. Unlike most substances, water expands when it freezes due to the formation of a crystalline structure that occupies more space than liquid water. At standard atmospheric pressure, this phase change causes roughly a 9% volume increase near 0ยฐC. This expansion can exert significant pressure on surrounding materials, which is why water pipes can burst in freezing temperatures. Understanding the expansion of water when it freezes is important in various fields, including engineering, meteorology, and environmental science.

How to Calculate Frozen Water Expansion?

The following steps outline how to calculate the expansion of frozen water.

  1. First, determine the initial liquid-water volume (Vwater).
  2. Next, select or measure appropriate densities for liquid water (ฯwater) and ice (ฯice) at the temperature/pressure of interest (or use the presets in the calculator).
  3. Calculate the ice volume using Vice = Vwater ยท (ฯwater/ฯice).
  4. Compute the percent increase as (Vice/Vwater โˆ’ 1) ร— 100% (typically about 9% near 0ยฐC at 1 atm).
  5. If freezing occurs in a container, compare the expanded volume to container capacity to estimate required headspace or overflow.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Initial Water Volume (Vwater) = 1 mยณ

Water Density (ฯwater) = 1000 kg/mยณ

Ice Density (ฯice) = 917 kg/mยณ โ†’ Ice Volume (Vice) โ‰ˆ 1 ร— (1000/917) = 1.0905 mยณ (about a 9.05% increase)