How to Convert Temperature Between Celsius, Fahrenheit, and Kelvin

The three formulas that cover almost every student and lab conversion:

• °F = °C × 9/5 + 32
• °C = (°F − 32) × 5/9
• K = °C + 273.15 (so °C = K − 273.15)

9/5 is exactly 1.8. 5/9 is exactly 1/1.8. Use fractions if you are writing a proof; 1.8 is fine in a spreadsheet if you keep the 32.

Points on the scale versus intervals

A reading is a point: the oven is 180 °C, the freezer is 0 °F, the lab bath is 298.15 K.

A change is an interval: the bath rose 5 °C, the specification allows ±2 K, the day warmed 9 °F.

For a reading, apply the full formula, including +32 or −32.

For an interval, convert only with the slope:

• Δ°F = Δ°C × 9/5
• Δ°C = Δ°F × 5/9
• ΔK = Δ°C

A specification of “±5 °C” is ±9 °F, not ±5 °F, and it is ±5 K. Treating 25 °C ± 5 °C as 77 °F ± 5 °F understates the band.

Why Kelvin exists in the problem set

The kelvin is the SI unit. One kelvin has the same size as one degree Celsius. Absolute zero is 0 K. Ice point is 273.15 K, not 273 K, unless the problem says to use 273.

The ideal-gas law PV = nRT uses T in kelvin. Putting 25 (meaning 25 °C) into RT is a classic zero-score. 25 °C is 298.15 K. R = 8.314 J/(mol·K) is already in kelvin; it does not “also work” in Celsius.

Boiling water at 1 atm is 100 °C = 373.15 K = 212 °F. That is a calibration check, not a conversion trick: if your Fahrenheit formula does not return 212 from 100, you inverted 5/9.

One numeric check: 37 °C

Clinical “normal” is often quoted as 37 °C.

°F = 37 × 9/5 + 32 = 66.6 + 32 = 98.6 °F.

K = 37 + 273.15 = 310.15 K.

Reverse: 98.6 °F → (98.6 − 32) × 5/9 = 66.6 × 5/9 = 37 °C. If you subtract 32 after multiplying, you get a number that looks vaguely medical and is wrong.

Room temperature used as 21 °C is 69.8 °F and 294.15 K. “70 °F” is 21.11 °C, close enough for HVAC talk and sloppy for a calorimetry blank.

Use temperature converter to confirm 37 → 98.6 and 310.15. The page runs in the browser; no account.

Rankine and the leftover scales

US engineering texts sometimes use Rankine: T(°R) = T(°F) + 459.67. A Rankine degree matches a Fahrenheit degree; the zero is absolute. If a steam table is in °R, do not feed those numbers to a Celsius–kelvin converter and hope. Convert °R → °F first (subtract 459.67), then to °C or K, or use a tool that lists Rankine.

Réaumur and “gas mark” are cooking or historical. They are not SI. Do not invent a linear map from gas mark to °C without a cooker chart; oven thermostats are already approximate.

Energy is a different page

Heat capacity problems produce joules, calories, or kWh, not a new temperature scale. Converting 4.184 J to calories is an energy job. Converting the temperature of the water from 20 °C to 68 °F is this page. How to convert energy and power is the sibling. The ideal gas law article is where T in kelvin actually gets used.

What to copy out of the converter

Copy the number and the scale. 310.15 without K will be pasted into a Celsius field. Negative kelvin is a data-entry bug, not a physical state. Below −273.15 °C the converter can still do arithmetic; nature cannot.

If you only needed a weather conversion, Fahrenheit ↔ Celsius is enough. If the next line of the lab is ΔU or q = mcΔT, keep ΔT in °C or K (same size) and leave Fahrenheit out of the energy equation unless every constant is in BTU and °F.