Water Density at Temperature: Formula and Calculator

Calculate pure water’s density from its temperature in degrees Celsius: enter a value from 0 to 100 °C to get density in kilograms per cubic metre (kg/m³), with the equivalent in grams per millilitre (g/mL). This calculator uses an empirical equation for liquid water near atmospheric pressure; it does not account for dissolved substances or pressure changes.

Formula

The calculator uses an empirical approximation for pure liquid water at standard atmospheric pressure:

ρ = 1000 × [1 − ((T + 288.9414) / (508929.2 × (T + 68.12963))) × (T − 3.9863)²]

• ρ is water density in kilograms per cubic metre (kg/m³).
• T is water temperature in degrees Celsius (°C).

To convert the result to grams per millilitre, divide kg/m³ by 1000: 1 kg/m³ = 0.001 g/mL. The second calculator result applies this conversion. The equation is an empirical fit, not a fundamental law; its displayed precision should not be mistaken for measurement accuracy.

Worked Example

With the default temperature, T = 20 °C:

1. Find the temperature difference from the density maximum: 20 − 3.9863 = 16.0137 °C.
2. Square it: 16.0137² ≈ 256.4386.
3. Evaluate the coefficient: (20 + 288.9414) ÷ [508929.2 × (20 + 68.12963)] ≈ 0.000006883.
4. Calculate density: 1000 × [1 − (0.000006883 × 256.4386)] ≈ 998.207 kg/m³.
5. Convert units: 998.207 ÷ 1000 ≈ 0.99821 g/mL.

The calculator rounds the first result to 998.207 kg/m³ and the converted result to 0.99821 g/mL.

Why Water Density Changes with Temperature

Density is mass divided by volume. Heating most liquids makes their molecules move more vigorously and occupy slightly more space, so their density falls. Water behaves unusually near freezing: its density is greatest at about 3.98 °C, then decreases as it cools toward 0 °C. The equation reflects this peak through the squared temperature difference from 3.9863 °C.

At 0 °C, liquid water is about 999.84 kg/m³; near 4 °C it is about 999.97 kg/m³; at 20 °C it is about 998.21 kg/m³; and at 100 °C it is about 958.35 kg/m³. These are approximate values for pure liquid water under the equation’s pressure assumption. Ice is less dense than liquid water, which is why it floats; this calculator does not calculate ice density.

When to Use the Result

Temperature-based density estimates are useful when converting between a water volume and its mass, comparing measurements, or understanding why a fixed volume of warm water weighs slightly less than the same volume of cooler water. For example, one litre of water at 20 °C has a mass of roughly 0.9982 kg, rather than exactly 1 kg.

For practical conversions, multiply volume by density:

• Mass in kg = volume in m³ × density in kg/m³.
• Mass in g = volume in mL × density in g/mL.

One cubic metre contains 1,000 litres, and one litre contains 1,000 millilitres. In US customary terms, one US liquid gallon is about 3.785 litres, and one kilogram is about 2.205 pounds. Keep units consistent: convert the volume to match the density units before multiplying. The mass of a measured quantity also depends on the actual temperature and composition of the sample.

Assumptions and Limits

The input range is limited to 0–100 °C, covering liquid water from its usual freezing point to its boiling point at approximately one atmosphere. The equation is intended for pure water near that pressure. It is not a general-purpose model for steam, ice, brine, or water under high pressure. At different pressures, the boiling point changes and density may also shift.

Salts and other dissolved substances change density; seawater, for example, is generally denser than pure water at the same temperature. If accuracy matters, use a reference table or measurement method suitable for the sample’s pressure, composition, and temperature. A temperature reading that is off by several degrees can matter more than the final decimal places shown by the calculator.

Common Mistakes

• Assuming 1,000 kg/m³ at every temperature: this is a convenient approximation, not an exact value. Water’s density varies with temperature.
• Confusing density with weight: density is mass per volume. Weight is a force and depends on gravity; a density result alone is not a weight.
• Mixing units: kg/m³ cannot be multiplied directly by a volume in litres without converting units. Use 0.001 m³ per litre, or convert density to kg/L.
• Over-reading decimals: three or five decimal places are calculation output, not a guarantee that a sample or thermometer is accurate to that level.
• Using Celsius values as Fahrenheit: convert Fahrenheit to Celsius first: °C = (°F − 32) × 5/9.

Frequently Asked Questions

What is the density of water at 20 °C?
For pure liquid water near atmospheric pressure, it is about 998.207 kg/m³, or 0.998207 g/mL.

At what temperature is water most dense?
Liquid water reaches its maximum density at approximately 3.98 °C, close to 999.97 kg/m³ at standard atmospheric pressure.

Is water density always 1 g/mL?
No. One g/mL is a useful approximation. Density varies with temperature and dissolved material; pure water is close to, but not exactly, 1 g/mL at ordinary room temperature.

How do I calculate water mass from volume?
Multiply volume by density after making the units compatible. For example, multiply litres by density in kg/L to obtain mass in kilograms.

Does this calculator work for seawater?
No. Dissolved salts make seawater denser than pure water, and its density also depends on temperature and salinity. Use a seawater-specific calculation or reference data for that sample.

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in t | Temperature | °C | 20 | 0 | 100
out rho | Water density | kg/m³ | 1000 * (1 - ((t + 288.9414) / (508929.2 * (t + 68.12963))) * (t - 3.9863)^2) | 3
out gml | Density | g/mL | rho / 1000 | 5