Ask a search engine to convert 10 °C to Fahrenheit and it answers 50 °F. Ask how much warmer a day is when the forecast says "10 degrees warmer" in Celsius, and the right answer is 18 °F. Both numbers are correct. They answer two different questions, and mixing them up is the most common temperature conversion error in print.
A Reading and a Difference Are Different Numbers
Celsius and Fahrenheit differ in two ways. Their degrees are different sizes, and their zeros sit in different places. A Fahrenheit degree is 5/9 of a Celsius degree, and 0 °C lines up with 32 °F.
A reading, the number on a thermometer, needs both corrections. That is why the familiar formula has two parts: °F = °C × 9/5 + 32. The multiplication fixes the degree size and the +32 moves the zero.
A difference between two readings has no zero to move. If the morning is 10 °C and the afternoon is 20 °C, the rise is 10 Celsius degrees, and in Fahrenheit the same two readings are 50 °F and 68 °F, a rise of 18. The +32 appears in both readings and cancels when you subtract. Only the 9/5 survives, so a change of 10 °C is a change of 18 °F.
Common Differences, Converted Correctly
Each row converts a change, so only the degree size applies: 1 °C of change is 1.8 °F and exactly 1 K.
| Where you see it | Celsius | Fahrenheit | Kelvin |
|---|---|---|---|
| Thermostat tolerance | ±0.5 °C | ±0.9 °F | ±0.5 K |
| Paris Agreement target | 1.5 °C | 2.7 °F | 1.5 K |
| Fever above normal | 2 °C | 3.6 °F | 2 K |
| "10 degrees warmer" | 10 °C | 18 °F | 10 K |
| Day to night in a desert | 25 °C | 45 °F | 25 K |
Where the Mistake Shows Up
The error has a recognisable signature: a small change in Celsius becomes a number in the thirties or forties in Fahrenheit. Translate a 1.5 °C warming limit with the reading formula and you get 34.7 °F, which would describe a frozen planet rather than a slightly warmer one. Run a ±2 °C manufacturing tolerance through it and the part is suddenly allowed to drift by ±35.6 °F.
The reverse happens too. A recipe that says to lower the oven by 25 °F becomes "lower it by −3.9 °C", because (25 − 32) × 5/9 is negative. The correct change is 13.9 °C, or about 14.
Kelvin and Celsius share a degree size, so a change in one is the same number in the other. That is why scientific papers often state differences in kelvin even when the readings are in Celsius: a 3 K rise cannot be mistaken for a reading.
The −40 crossover
Because the two scales have different degree sizes, their lines cross once. Setting °C equal to °C × 9/5 + 32 and solving gives −40, so −40 °C and −40 °F are the same temperature. Above it a Fahrenheit reading is always the larger number, below it the Celsius one is.
Where Each Scale Put Its Zero
None of the zero points on the common scales was chosen for the arithmetic. They come from whatever the inventor could reproduce in a workshop.
Fahrenheit, 1724
Daniel Gabriel Fahrenheit set 0 at the coldest mixture he could make reliably, ice, water and ammonium chloride, and placed melting ice at 32 and body temperature at 96. The scale was recalibrated after his death so that water boils at 212, which is why normal body temperature drifted to 98.6.
Celsius, 1742
Anders Celsius used 100 steps between the freezing and boiling points of water, but ran the scale upside down, with 0 for boiling and 100 for freezing. It was flipped to its present direction within a few years of his death. The name centigrade was officially replaced by Celsius in 1948.
Kelvin, 1848
William Thomson, later Lord Kelvin, argued in 1848 for an absolute scale that did not depend on any particular substance, and estimated absolute zero at about −273 °C. The scale named after him counts Celsius-sized degrees up from that point. Since 1967 its unit has been the kelvin, written K with no degree sign, and since 2019 it has been defined by fixing the Boltzmann constant at exactly 1.380649 × 10⁻²³ J/K.
Rankine, 1859
William Rankine did the same for Fahrenheit: Fahrenheit-sized degrees counted from absolute zero, so 0 °R is −459.67 °F. American engineering thermodynamics still uses it, because gas laws need an absolute scale and the inputs are often in Fahrenheit.
Convert a reading or a change
Celsius, Fahrenheit, Kelvin, Rankine and Réaumur, with the formula under every result.
"Twice as Hot" Only Works in Kelvin
Because the Celsius and Fahrenheit zeros are arbitrary, ratios of their readings mean nothing. 20 °C is not twice as hot as 10 °C. In kelvin the two are 293.15 K and 283.15 K, so on an absolute scale the warmer day is about 3.5% hotter, not 100%. In Fahrenheit the same pair reads 68 and 50, which suggests 36% more, and that is just as wrong.
Anything that multiplies or divides temperatures, such as the ideal gas law, radiated heat or the efficiency of an engine, has to use kelvin or Rankine. Adding and subtracting can use any scale, as long as the result is labelled as a difference.
Two Reference Points That Are Not Quite Exact
Since the Celsius scale was tied to kelvin, water no longer defines it. Under the International Temperature Scale of 1990, pure water at standard sea-level pressure boils at about 99.974 °C, a hair under 100. For cooking and weather the difference is invisible, but calibration labs do not use boiling water as a 100 °C reference.
Body temperature is looser still. The figure of 98.6 °F comes from Carl Wunderlich's 1868 average of 37 °C, converted to Fahrenheit with more precision than the original ever claimed. A 1992 study by Philip Mackowiak and colleagues in JAMA measured healthy adults at an average oral temperature of 36.8 °C, or 98.2 °F, and put the upper limit of normal at 37.7 °C rather than 38 °C.
Converting in Your Head
For weather, double the Celsius and add 30. It is exact at 10 °C (50 °F) and stays within a few degrees across everyday temperatures: 20 °C gives 70 against a true 68, and 30 °C gives 90 against 86. Going the other way, subtract 30 and halve.
For a change, drop the 30 entirely. Doubling the Celsius figure overshoots the Fahrenheit change by about 10%, which is close enough for a forecast. Multiply by 1.8 for the exact number.
Frequently Asked Questions
Related Tools
Keep Reading
Length Units: The Inch Is Defined in Metres, and Other Surprises
Every imperial unit has been legally metric since 1959. Where the US survey foot differed until 2023, and the conversion error that lost a Mars orbiter.
GB or GiB: Why a 1 TB Drive Shows Up as 931 GB
A terabyte drive holds 10¹² bytes, and Windows divides by 1,024 before calling it 931 GB. The 1999 standard that named the binary units, and why Macs disagree.
Percentage Change vs Percentage Points, and Other Costly Confusions
Down 50 percent then up 50 percent leaves you down 25. Why percentages are not symmetric, and how stacked discounts really multiply.
Why 1/3 Never Ends: Fractions, Decimals and Common Denominators
1/8 ends after three digits and 1/3 never does. The prime-factor rule behind terminating decimals, why 1/7 cycles through six digits, and why 0.1 + 0.2 misbehaves.