Celsius to Fahrenheit Formula, Explained Step by Step

The formula, both ways

°F = °C × 9/5 + 32

°C = (°F − 32) × 5/9

9/5 is the same as 1.8, so you can also write the first formula as °F = °C × 1.8 + 32. Going the other way, multiplying by 5/9 is the same as dividing by 1.8. The order matters: from Celsius you multiply first, then add 32; from Fahrenheit you subtract 32 first, then multiply. Each direction undoes the other in reverse order.

Worked examples: Celsius to Fahrenheit

Each example uses the same three steps. Multiplying by 9 and then dividing by 5 keeps the arithmetic in whole numbers more often than multiplying by 1.8 does, which makes it easier to check by hand.

25 °C to Fahrenheit (a warm spring or summer day)

1. Multiply by 9: 25 × 9 = 225
2. Divide by 5: 225 ÷ 5 = 45
3. Add 32: 45 + 32 = 77

Result: 25 °C = 77 °F.

37 °C to Fahrenheit (a decimal result)

1. Multiply by 9: 37 × 9 = 333
2. Divide by 5: 333 ÷ 5 = 66.6
3. Add 32: 66.6 + 32 = 98.6

Result: 37 °C = 98.6 °F.

100 °C to Fahrenheit (water boiling at sea level)

1. Multiply by 9: 100 × 9 = 900
2. Divide by 5: 900 ÷ 5 = 180
3. Add 32: 180 + 32 = 212

Result: 100 °C = 212 °F.

−40 °C to Fahrenheit (the point where both scales meet)

1. Multiply by 9: −40 × 9 = −360
2. Divide by 5: −360 ÷ 5 = −72
3. Add 32: −72 + 32 = −40

Result: −40 °C = −40 °F.

180 °C to Fahrenheit (a standard oven setting for cakes)

1. Multiply by 9: 180 × 9 = 1620
2. Divide by 5: 1620 ÷ 5 = 324
3. Add 32: 324 + 32 = 356

Result: 180 °C = 356 °F.

The −40 example is a useful self-check: if your method turns −40 °C into anything other than −40 °F, a sign or a step has gone wrong.

Reverse examples: Fahrenheit to Celsius

For the opposite direction, take away the 32 first, then scale by 5/9. The Fahrenheit to Celsius converter shows the same working for any value you type.

The quick mental trick: double it and add 30

To estimate Fahrenheit in your head, double the Celsius number and add 30. For 20 °C: 20 × 2 = 40, plus 30 is 70, so about 70 °F. The exact answer is 68 °F, so the shortcut is 2 degrees high.

The shortcut uses 2 instead of 1.8 and 30 instead of 32, so its error changes steadily: it is exact at 10 °C and drifts by 0.2 °F for every degree Celsius you move away from that point. Between about 0 °C and 20 °C it is within 2 °F, which is fine for deciding whether you need a jacket. At −20 °C it reads 6 °F too low, and for an oven at 180 °C it overshoots by 34 °F, which is enough to burn a cake.

For a precise result without a calculator, use this version: double it, subtract a tenth of that, then add 32. For 25 °C: 25 × 2 = 50, take away 5 to get 45, then add 32 to get 77. This method is exact because doubling and removing a tenth is the same as multiplying by 1.8.

Why 9/5 and why 32?

Both scales are pinned to the freezing and boiling points of water at sea level. Celsius puts them at 0 and 100, a gap of 100 degrees. Fahrenheit puts them at 32 and 212, a gap of 180 degrees. Because 180 ÷ 100 = 1.8 = 9/5, a Fahrenheit degree is smaller than a Celsius degree: every Celsius degree equals 1.8 Fahrenheit degrees.

The 32 is there because the two scales start counting from different places. Water freezes at 0 on one scale and at 32 on the other, so after scaling you still have to shift the result up by 32. Daniel Gabriel Fahrenheit set his zero in the early 1700s using a cold mixture of ice, water and salt, long before Anders Celsius proposed a 100-step scale based on water.

Plot the formula on a graph and you get a straight line with a slope of 9/5 that crosses the Fahrenheit axis at 32. That is why the conversion is called linear, and why teachers use it to introduce the equation y = mx + c.

Common mistakes

• Adding 32 before multiplying. (25 + 32) × 9/5 gives 102.6, not 77. Multiply first.
• Using 5/9 instead of 9/5. Fahrenheit numbers are larger than Celsius above −40, so the fraction going from °C to °F must be greater than one.
• Converting a change with the full formula. A rise of 10 °C is a rise of 18 °F. Do not add 32 to a difference, only to an actual reading.
• Forgetting the minus sign. For −10 °C: −10 × 9/5 = −18, and −18 + 32 = 14 °F. Dropping the sign gives 50 °F, which is far too warm.
• Rounding too early. Keep the decimals until the last step, then round. The printable conversion chart lists every value to two decimals if you want to check your work.

Need the formula in a spreadsheet or a program? See the formula in Excel, Python and JavaScript, or practise with the conversion worksheet.