Celsius to Fahrenheit Converter

How to convert Celsius to Fahrenheit (the formula)

The formula is °F = °C × 9/5 + 32, which is the same as multiplying by 1.8 and adding 32. The 9/5 reflects that a Fahrenheit degree is smaller than a Celsius degree, there are 180 Fahrenheit degrees between freezing and boiling, but only 100 Celsius degrees. The +32 shifts the scales so that 0 °C lines up with 32 °F.

Two examples: 20 °C × 1.8 = 36, plus 32 = 68 °F. And 37 °C × 1.8 = 66.6, plus 32 = 98.6 °F, normal body temperature. Because both steps are simple, you can do most conversions in your head with a little practice.

This page converts live in both directions. Type a Celsius value and the Fahrenheit box fills in; type Fahrenheit and the Celsius updates instead. That makes it easy to check a weather forecast, an oven setting or a fever reading without retyping.

Why Fahrenheit and Celsius cross at −40 degrees

There is exactly one temperature where the Celsius and Fahrenheit scales show the same number: −40. Plug −40 into the formula and you get −40 × 1.8 = −72, plus 32 = −40 °F. The two scales meet there because they have different zero points (0 °C vs 32 °F) and different degree sizes (100 vs 180 between the same two fixed points).

Geometrically, the two scales are two straight lines on a temperature-versus-reading graph. Because they have different slopes, they must cross somewhere, and the algebra puts that crossing at −40. Everywhere above −40, the Fahrenheit reading is the larger number; everywhere below it, Fahrenheit reads colder than Celsius.

This is a favorite trivia question, but it is also a genuinely useful check: if you convert −40 °C and get anything other than −40 °F, your formula is wrong. It is the single best sanity test for the Celsius-to-Fahrenheit relationship.

Celsius to Fahrenheit conversion chart

These are the Celsius temperatures US users look up most, converted with the exact formula.

Anchor points worth memorizing: 0 °C is 32 °F, 20 °C is 68 °F, and 100 °C is 212 °F. From those three you can estimate almost anything in between.

Worked examples: weather, body temperature and baking

Four Celsius-to-Fahrenheit conversions with real-world meaning.

• Weather: a 30 °C forecast is 30 × 1.8 + 32 = 86 °F, a hot summer day in the US.
• Fever: 38 °C is 38 × 1.8 + 32 = 100.4 °F, the usual threshold for a fever.
• Baking: 180 °C is 180 × 1.8 + 32 = 356 °F, a standard cake temperature.
• Freezing: 0 °C is 0 × 1.8 + 32 = 32 °F, the freezing point of water.

The fever example is a good one to remember: because a Celsius degree is 1.8 times a Fahrenheit degree, a small Celsius change is a bigger Fahrenheit change. A rise from 37 to 38 °C is only one degree Celsius but 1.8 degrees Fahrenheit.

Celsius to Fahrenheit in the kitchen: oven temperatures

Recipes from Europe, Australia and Canada list oven temperatures in Celsius, while US ovens are marked in Fahrenheit. The conversion is the same formula, but bakers usually round to a familiar setting.

A few common translations: 160 °C = 320 °F, 180 °C = 356 °F (usually set to 350 °F), 200 °C = 392 °F (usually 400 °F), and 220 °C = 428 °F (usually 425 °F). Most US ovens let you pick from steps of 25 °F, so you round the exact conversion to the nearest mark. A 5 °F difference is negligible for most baking.

Fan-assisted (convection) ovens run hotter, so many recipes reduce the temperature by about 20 °C (roughly 25-50 °F) when a fan is used. That adjustment is separate from the unit conversion, convert first, then apply any fan reduction the recipe mentions.

Candy and bread recipes are less forgiving than cakes, so for those it is worth using the exact converted value rather than rounding to the nearest 25 °F.

Common Celsius-to-Fahrenheit mistakes

Nearly all Celsius-to-Fahrenheit errors trace back to one of these slips.

• Forgetting to add 32. Multiplying by 1.8 alone gives the size of the temperature interval but not the reading. 20 °C is not 36 °F; it is 68 °F.
• Adding 32 before multiplying. The order matters. Always multiply by 9/5 first, then add 32.
• Multiplying by 5/9 instead of 9/5. That is the Fahrenheit-to-Celsius direction. Going C to F makes the number bigger, not smaller.
• Using the +30 shortcut as exact. "Double and add 30" is a rough estimate that drifts a few degrees; use it for a ballpark, not for baking or medicine.

The −40 test is the fastest way to catch a reversed formula: if −40 °C does not convert to −40 °F, your operation is backwards.

Celsius vs Fahrenheit: why both scales exist

Celsius and Fahrenheit are the two temperature scales in everyday use, and they came from different scientific traditions.

Daniel Gabriel Fahrenheit built his scale in 1724 around three reference points: the freezing point of a brine mixture, the freezing point of water, and human body temperature. He set the brine point at 0 and body temperature near 96, which is why water freezes at 32 °F and boils at 212 °F, exactly 180 degrees apart. Anders Celsius proposed his scale in 1742 with 0 at the freezing point and 100 at the boiling point of water, which is why it is also called the centigrade scale.

Because both scales use water's freezing and boiling points as their fixed reference, the distance between those two points is 100 degrees on the Celsius scale and 180 degrees on the Fahrenheit scale. That ratio of 100:180 simplifies to 5:9, which is where the 9/5 factor in the conversion formula comes from. The two scales are different rulers laid over the same physical reality, and once you know the freezing and boiling anchors (0/32 and 100/212) the formula is easy to remember.

Sources: NIST SP 811, Guide for the Use of the International System of Units (SI), BIPM SI Brochure (the official definition of the SI), NIST SI Units reference.

Where these conversion factors come from

The relationship between the Celsius and Fahrenheit scales is fixed by international agreement rather than by local convention. The values used on this page follow the NIST guide to the SI (US Department of Commerce) and the BIPM SI Brochure, the two documents that define the exact values used worldwide.

Because these factors are exact by definition rather than measured, converting a number and converting it back always returns the number you started with, there is no rounding drift to worry about.