Hong Life CalculatorsUnderstanding the water density calculator — concept and principle
The density of water changes slightly with temperature, and it matters in laboratory work, calibrating glassware, specific gravity measurements and fluid calculations. This calculator gives the density of pure, air-free water between 0 and 40 °C using the internationally recommended formula of Tanaka et al. (2001), plus the specific volume, the density in lb/ft³ and the mass of a chosen volume.
How it is calculated
ρ = a₅ × [1 − (t + a₁)² (t + a₂) ÷ (a₃ (t + a₄))]
- a₁ = −3.983035 °C, a₂ = 301.797 °C, a₃ = 522,528.9 °C², a₄ = 69.34881 °C, a₅ = 999.974950 kg/m³.
- t is the temperature in °C (0–40 °C).
- Specific volume = 1000 ÷ ρ (cm³/g); lb/ft³ = ρ × 0.0624279606; mass of V litres = ρ × V ÷ 1000.
- The last row shows how far the density is below the maximum, a₅.
The principle
Most liquids become steadily denser as they cool, but water is unusual. As it cools towards about 4 °C its molecules pack more tightly, but below that, hydrogen bonds begin to form an open, ice-like structure, so the density falls again. The maximum density, 999.975 kg/m³, occurs at about 3.98 °C. The formula captures this curve: the squared term (t − 3.98)² is zero at the maximum and grows on either side. That is why lakes in winter have 4 °C water at the bottom and ice on top.
Worked example
Default inputs: 20 °C, volume 1 L.
- t + a₁ = 20 − 3.983 = 16.017; squared = 256.54.
- t + a₂ = 321.797; a₃(t + a₄) = 522,528.9 × 89.349 = 46,687,000 (approximately).
- Fraction = 256.54 × 321.797 ÷ 46,687,000 = 0.0017683.
- ρ = 999.97495 × (1 − 0.0017683) = 998.207 kg/m³ = 0.998207 g/cm³.
- Specific volume = 1.0018 cm³/g; 62.316 lb/ft³; 1 L has a mass of 0.9982 kg; this is 1.768 kg/m³ below the maximum.
| Water temperature (°C) | Density of water (kg/m³) |
|---|---|
| 5 | 999.967 |
| 10 | 999.703 |
| 15 | 999.103 |
| 20 | 998.207 |
| 25 | 997.047 |
| 30 | 995.649 |
| 40 | 992.215 |
How to read the result
For most everyday work, water's density can be taken as 1,000 kg/m³, but the 0.18 % difference at 20 °C matters when calibrating pipettes or volumetric flasks by weighing water. Dissolved air lowers density very slightly, while dissolved salts raise it noticeably: sea water is about 1,025 kg/m³. Pressure also increases density slightly.
Common mistakes
- Using the formula outside 0–40 °C.
- Applying it to tap water or sea water without correcting for dissolved salts.
- Assuming the maximum density is at exactly 4 °C; it is at about 3.98 °C.
Frequently asked questions
At what temperature is water densest?
At about 3.98 °C, where its density is about 999.975 kg/m³.
Why does ice float?
Ice is about 8 % less dense than liquid water because its crystal structure is more open.
Is 1 litre of water exactly 1 kg?
Only approximately; at 20 °C it is about 0.998 kg.
How dense is water at 100 °C?
About 958 kg/m³, but that is outside this formula's range.
Sources: Tanaka M., Girard G., Davis R., Peuto A., Bignell N., "Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports", Metrologia 38 (2001) 301–309