Estimate how long water takes to freeze in a freezer from the amount of water, its starting temperature and the container type, using typical values.
- Ice Melting Time Calculator
- All Physics Calculators
- Freezing Point Calculator
- Dry Ice Calculator
- Boiling Point Calculator (Water)
Water Freeze Time Formula
- t = total idealized time in seconds; divide by 60 for minutes or 3,600 for hours
- m = approximate water mass (kg); this model uses a constant density of 1,000 kg/m³, or 1 kg/L
- c = specific heat of water: 4,186 J/(kg·°C)
- Ti = initial liquid temperature from 0 to 100°C at normal pressure
- Lf = latent heat of fusion: 334,000 J/kg
- UA = effective overall thermal conductance (W/K); Tf = constant ambient temperature below 0°C and above absolute zero
The model first cools spatially uniform liquid water to 0°C using Newton cooling: tc = (m c / UA) × ln((Ti − Tf)/(−Tf)). It then removes latent heat at 0°C: tfreeze = m Lf / (UA × (−Tf)). The total is their sum. Pick a container type to use typical still-air values, supply a known or calibrated UA, or compute UA from an effective overall coefficient times area. Geometric mode uses A = factor × volume(2/3), with SI units; the default factor 6 is the full surface of a cube. Container presets give typical estimates only; the share of freezer space does not establish UA. The inverse solves this monotone equation by bisection. Numerical support excludes temperatures within 0.000001°C of 0°C or absolute zero.
Historical Illustrative Freeze-Time Ranges
The old page listed the following unsourced illustrative ranges. They are retained as historical examples, not validated measurements, calibration data or outputs of the new model. Freezer air around −18°C (−0.4°F) alone cannot determine freezing time without effective heat-transfer information.
| Container | Volume | Legacy illustrative range |
|---|---|---|
| Ice cube (aluminum tray) | 30 mL | 2-3 hours |
| Ice cube (silicone tray) | 30 mL | 3-5 hours |
| 75 mm cocktail ice sphere | 220 mL | 6-8 hours |
| 12 oz / 355 mL bottle | 355 mL | 5-8 hours |
| 1 L water bottle | 1,000 mL | 8-12 hours |
| 2 L water bottle | 2,000 mL | 14-24 hours |
| 1-gallon jug | 3,785 mL | 24-48 hours |
What Controls Freeze Time
Container Material and Thermal Conductivity
Heat transfer depends on wall thickness, area, contact and air-side resistance as well as material conductivity. The approximate material figures below vary with grade and temperature and do not determine freezing speed or supply the calculator’s effective coefficient. A growing ice layer can add resistance that the constant-UA model omits.
| Material | Thermal Conductivity (W/(m·K)) |
|---|---|
| Aluminum | 205 |
| Stainless steel | 16 |
| Borosilicate glass | 1.1 |
| Polypropylene (plastic) | 0.22 |
| Silicone | 0.17 |
Surface Area to Volume Ratio
For geometrically similar containers with the same effective coefficient, more exposed area per unit volume increases UA per kilogram. A cube containing 30 cm³ has a side near 3.107 cm and full-surface SA:V near 1.931 cm⁻¹. A 1 L cube has a 10 cm side and SA:V of 0.6 cm⁻¹. Actual bottles and trays need their own dimensions and effective exposed area; those ratios alone do not predict household freeze times.
Forced vs. Still Air Convection
Air circulation can change heat transfer, but no universal freezer coefficient or percentage time reduction is assumed here. An air-convection coefficient alone may omit container, contact and ice resistance. Use an effective overall value appropriate to the actual setup, and recognize that freezer cycling, changing airflow and available cooling capacity are outside this model.
Water Purity and Nucleation
This model assumes equilibrium freezing of pure water at 0°C under normal pressure. It excludes supercooling, nucleation delay, dissolved substances and evaporation. Sudden visible crystal growth does not establish that all the required latent heat has already been removed.
The Mpemba Effect
Mpemba and Osborne published their hot-water freezing observations in 1969. The constant-UA model used here does not reproduce Mpemba effects: with the same mass, conductance and ambient temperature, increasing the initial liquid temperature increases the modeled cooling time.
Real experiments can involve changing heat transfer, evaporation, temperature gradients and nucleation conditions that are absent from this simplified calculation. The calculator provides no hot-water shortcut or guaranteed freezing schedule.
Example Calculation
For an explicit model example, how long does 1 L of water at 20°C take to complete ideal freezing at a constant −18°C ambient when effective UA is assumed to be 1 W/K?
Step 1 – Model mass: 0.001 m³ × 1,000 kg/m³ = 1 kg (approximate constant-density assumption).
Step 2 – Total heat to extract: Q = 1.0 x (4,186 x 20 + 334,000) = 417,720 J
Step 3 – Liquid cooling time = 4,186 × ln(38/18) ≈ 3,127.8395 seconds. Ideal phase-change rate = UA × 18 K = 18 W, so phase-change time = 334,000/18 ≈ 18,555.5556 seconds.
Step 4 – Total idealized time ≈ 21,683.395 seconds, or 6.0232 hours. This ends with frozen water at 0°C, before cooling the ice further.
This example uses a hypothetical supplied UA, not an empirical household preset. The model assumes nearly uniform liquid temperature, fixed area, constant properties and constant overall conductance. It excludes moving ice-front resistance, container heat capacity, nucleation delay and freezer cycling. Actual freezing times can differ substantially; the inverse temperature is a model solution, not a recommended freezer setting.
