Final temperature of mixing calculator

The Final temperature of mixing calculator computes final temperature of mixing from the relation Tf = (m1 c1 T1 + m2 c2 T2)/(m1 c1 + m2 c2). It takes 6 inputs (mass 1 in kg, specific heat 1 in J/kgK, temp 1 in C, mass 2 in kg, specific heat 2 in J/kgK, temp 2 in C) and returns the final temperature in C. Physics students, lab and workshop technicians, and hobbyist builders and observers who need one quantity in a standard physical relationship worked out from figures they already have, whether those come from an instrument reading, a datasheet, or a published table. Enter your values below and the result updates instantly, and you can share a permalink that pre-fills the exact calculation. Convert every value to one consistent set of units before entering it (lengths and masses on the same scale rather than metres mixed with centimetres, absolute temperatures in kelvin, angles in whatever unit the field asks for), respect the sign conventions that carry meaning, such as direction for velocity, acceleration and force or which side of a lens a distance is measured on, and quote the result to no more precision than your least precise input supports. For example, with mass 1 = 2 kg, specific heat 1 = 4186 J/kgK, temp 1 = 30 C, mass 2 = 1 kg, specific heat 2 = 4186 J/kgK, temp 2 = 60 C, the final temperature works out to 40 C, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. Units and physical constants follow NIST / CODATA; the relation itself is a standard result of physics, and the figure above each result carries the date it was last verified. Each of these relationships describes an idealised situation, so a result holds only as far as that idealisation does, whether the assumption is a point mass, a uniform field, an ideal component, a single uniform medium, no losses to friction or drag, or a steady rate, and a real measurement can depart from it once conditions stop matching the model.

With Mass 1 = 2 kg, Specific heat 1 = 4186 J/kgK, Temp 1 = 30 C, Mass 2 = 1 kg, Specific heat 2 = 4186 J/kgK, Temp 2 = 60 C, the result is 40 C.

Formula: Tf = (m1 c1 T1 + m2 c2 T2)/(m1 c1 + m2 c2). Source: NIST / CODATA, as at 2026-06-22.

Final temperature40 C

Applies to: any numeric inputs. Method source: NIST / CODATA, checked 2026-06-22.

The formula

Tf = (m1 c1 T1 + m2 c2 T2)/(m1 c1 + m2 c2)

Worked example

With Mass 1 = 2 kg, Specific heat 1 = 4186 J/kgK, Temp 1 = 30 C, Mass 2 = 1 kg, Specific heat 2 = 4186 J/kgK, Temp 2 = 60 C:

  1. Tf = (sum m c T)/(sum m c)
  2. Final temperature = 40 C

This worked example is one of the automated golden-value tests this calculator must pass before it can publish.

What this assumes

  • Inputs are real numbers in the units shown.
  • The result is the exact value of Tf = (m1 c1 T1 + m2 c2 T2)/(m1 c1 + m2 c2); general information, not professional advice.

Frequently asked questions

What formula does this use?

Tf = (m1 c1 T1 + m2 c2 T2)/(m1 c1 + m2 c2). This is a standard result of physics; units and physical constants follow NIST / CODATA.

Does the result ever change over time?

No. This is a pure formula with no external rate, so the same inputs always give the same result.

Official sources and verification

Reviewed by the CalculatorHub team, edited by James Graham, 2026-06-22. See our methodology. General information, not professional advice.