Calculate the final temperature when mixing hot and cold water, or find each volume needed for a target temperature, in °C, °F, and common volume units.

Estimate for liquid water (0–100°C, 32–212°F) assuming no heat loss.

Optional settings

Water Mixture Temperature Formula and Guide

The water temperature calculator finds the final temperature after mixing two amounts of water at different starting temperatures. Assuming equal specific heat and no external heat transfer, the result is a mass-weighted average. This calculator accepts volumes and additionally assumes equal density for the two water portions; that is an approximation. Its supported liquid-water input range is0–100°C (32–212°F), with no pressure or phase-change model.

WT = (m₁ × T₁ + m₂ × T₂) ÷ (m₁ + m₂)
Variable Meaning Common Units
WT Final mixed water temperature °C, °F, K
m1 Mass of the first water portion kg, g, lb
T1 Starting temperature of the first water portion °C, °F, K
m2 Mass of the second water portion kg, g, lb
T2 Starting temperature of the second water portion °C, °F, K

How the Calculation Works

Each water portion contributes thermal energy in proportion to its mass and temperature. A larger mass pulls the final temperature closer to its own starting temperature, which is why this is called a weighted average rather than a simple average.

  1. For final temperature, enter the hot and cold water volumes. For target volumes, choose that solve and enter the target temperature and total volume.
  2. Enter the starting temperature for each portion.
  3. Select the correct unit for each volume; each selector converts its current quantity.
  4. Select the correct scale for each temperature; the calculator normalizes them internally.
  5. Select Calculate for the idealized mixed temperature or required hot volume and cold-volume breakdown. Equal starting temperatures give a unique final temperature, but a matching target does not determine a unique split.

Rearranged Forms

The following are general mass-based algebraic references. The interface provides final temperature or hot/cold volumes for a known total and target; it does not solve for an unknown starting temperature. For equal densities, mass ratios can be replaced by volume ratios in consistent units.

Solve for the first temperature:

T₁ = [WT × (m₁ + m₂) − m₂ × T₂] ÷ m₁

Solve for the second temperature:

T₂ = [WT × (m₁ + m₂) − m₁ × T₁] ÷ m₂

Solve for the first mass:

m₁ = m₂ × (WT − T₂) ÷ (T₁ − WT)

Solve for the second mass:

m₂ = m₁ × (T₁ − WT) ÷ (WT − T₂)

Quick Interpretation Rules

  • The final temperature must fall between the two starting temperatures.
  • If one mass is much larger than the other, the final temperature will be much closer to the larger mass temperature.
  • If both masses are equal, the final temperature becomes the simple average of the two temperatures.
  • If both starting temperatures are the same, mixing does not change the temperature.

Equal-mass shortcut:

WT = (T₁ + T₂) / (2)

Example

If 200 g of water at 50°C is mixed with 100 g of water at 40°C, the ideal final temperature follows from the mass equation. In this volume-based calculator, entering200 mL and100 mL gives the same estimate under the equal-density assumption.

WT = (200 × 50 + 100 × 40) ÷ (200 + 100)
WT = 46.67^° C

This result is closer to 50°C than to 40°C because the hotter water has the greater mass.

When This Calculator Is Accurate

  • Both materials are liquid water.
  • No meaningful heat is lost to the air, pipes, or container.
  • No ice melting or boiling occurs during mixing.
  • The container itself does not absorb a significant amount of heat.
  • The selected unit must match each entered value; the calculator converts the quantities to a common scale.

Common Mistakes

  • Mixing temperature scales: Select the correct scale beside each input; the calculator performs the conversion.
  • Mixing mass and volume: The interface accepts volume units. The general mass equations above require consistent mass units; grams cannot be entered as if they were milliliters without a density assumption.
  • Using the formula for different liquids: This simplified form is for water-to-water mixing. Other substances require specific heat to be included.
  • Ignoring container heat loss: Real-world results may be slightly lower or higher if the container is hot or cold.
  • Using phase-change conditions: If ice or steam is involved, latent heat must be considered, so this simple model will not be sufficient.

Helpful Notes

For everyday estimating, many people think in terms of hot water and cold water amounts rather than energy. This calculator gives an idealized estimate for plain-water mixing. Heat loss, container temperature and changing water density can affect actual results; measure the mixed temperature before use.

Mass is the correct basis for precision calorimetry. This volume estimator assumes equal water density and specific heat; use mass-based energy calculations and appropriate heat-capacity data when that approximation is inadequate.