Celsius to Fahrenheit Formula: Shortcut, Examples, and a Chart

To convert Celsius to Fahrenheit, multiply by 9/5 (or 1.8), then add 32: F = C × 9/5 + 32. To convert Fahrenheit to Celsius, reverse the steps. Subtract 32 first, then multiply by 5/9: C = (F − 32) × 5/9. For example, 25 °C × 1.8 = 45, and 45 + 32 = 77 °F.

That answers the basic question. The rest of this guide explains where the 9/5 and the 32 come from. It also covers a mental shortcut that works without a calculator (and where it stops working), why −40 is the same on both scales, how Kelvin fits in, and a reference chart for weather, body, and oven temperatures.

If you just need a number right now, the temperature converter converts between Celsius, Fahrenheit, and Kelvin. If you want to do the math yourself, keep reading.

The Celsius to Fahrenheit formula, step by step

The formula has two parts because the two scales differ in two ways. Their degrees are different sizes, and they start counting from different points.

Why the formula uses 9/5 and 32

At standard sea-level pressure, water freezes at 0 °C and 32 °F, and it boils at roughly 100 °C and 212 °F. So the same physical range spans 100 Celsius degrees but 180 Fahrenheit degrees (212 − 32 = 180).

• The 9/5 handles size. 180 ÷ 100 = 1.8, which is 9/5. Each Celsius degree is 1.8 times as large as a Fahrenheit degree.
• The 32 handles the starting point. Water freezes at 0 on one scale and 32 on the other, so you shift by 32 after scaling.

(Strictly speaking, the modern Celsius scale is defined through the kelvin, not through water. That puts the boiling point at standard pressure a hair under 100 °C. For everyday use, 0 and 100 are the anchors that matter.)

Worked examples: Celsius to Fahrenheit

1. A warm day, 25 °C: 25 × 1.8 = 45, then 45 + 32 = 77 °F.
2. Body temperature, 37 °C: 37 × 1.8 = 66.6, then 66.6 + 32 = 98.6 °F.
3. A common oven setting, 180 °C: 180 × 1.8 = 324, then 324 + 32 = 356 °F.
4. A cold morning, −10 °C: −10 × 1.8 = −18, then −18 + 32 = 14 °F.

The order matters: multiply first, then add. If you add 32 first and then multiply, 25 °C becomes (25 + 32) × 1.8 = 102.6, which is wrong.

Fahrenheit to Celsius: reversing the formula

To go back, undo each step in reverse order. You added 32 last, so you subtract it first. Then you undo the multiplication by 9/5 by multiplying by 5/9, which is the same as dividing by 1.8.

C = (F − 32) × 5/9

Worked examples: Fahrenheit to Celsius

1. Room temperature, 68 °F: 68 − 32 = 36, then 36 × 5/9 = 180/9 = 20 °C.
2. A recipe calling for 350 °F: 350 − 32 = 318, then 318 × 5/9 = 1,590/9 ≈ 176.7 °C. Most cooks use 175 or 180 °C.
3. A hot day, 100 °F: 100 − 32 = 68, then 68 × 5/9 = 340/9 ≈ 37.8 °C.
4. Checking body temperature, 98.6 °F: 98.6 − 32 = 66.6, then 66.6 ÷ 1.8 = 37 °C.

Leaving out the parentheses is the classic mistake. Typing 68 − 32 × 5/9 into a calculator without them gives about 50.2, because the calculator multiplies before it subtracts. Either use parentheses or press equals after the subtraction. An online calculator that supports parentheses lets you type the formula exactly as written.

The double-and-add-30 shortcut (and how far off it gets)

For a quick estimate in your head, double the Celsius number and add 30. So 20 °C becomes 40 + 30 = 70 °F. The real answer is 68 °F, which is close enough to decide whether you need a jacket.

The shortcut works because 2 is near 1.8 and 30 is near 32. Those two small errors pull in opposite directions, and they cancel out exactly at 10 °C. The farther you move from 10 °C, the larger the gap.

Shortcut error at common temperatures

A simple rule explains the table. The error equals 0.2 × C − 2, which works out to 2 °F for every 10 °C away from 10 °C. For weather (roughly −10 to 35 °C), you'll be within about 5 °F. For ovens, the shortcut is useless, and 34 °F too hot can burn a cake.

The reverse version, subtract 30 and halve, behaves the same way: it's exact at 50 °F and drifts further off the further you go from there, about 1 °C for every 18 °F. Above 50 °F it gives too low an answer. For 86 °F, it gives (86 − 30) ÷ 2 = 28 °C, while the true value is 30 °C (86 is 36 °F above 50, and 36 ÷ 18 = 2 °C off). At 350 °F it gives 160 °C, about 16.7 degrees below the true 176.7 °C.

A mental method that's exact

If you want the real answer without a calculator, take a few more steps:

1. Double the Celsius value. For 25 °C, that's 50.
2. Subtract 10% of that result: 50 − 5 = 45. (Doubling and then taking away a tenth is the same as multiplying by 1.8.)
3. Add 32: 45 + 32 = 77 °F.

Going the other way, subtract 32, halve, then add a ninth of the result. If a ninth is awkward, adding about 10% gets you very close. For 68 °F: 68 − 32 = 36, half is 18, and adding a ninth (2) gives exactly 20 °C. For a refresher on taking 10% of a number in your head, see how to calculate percentages.

Why −40 is the same in Celsius and Fahrenheit

Only one temperature reads the same on both scales: −40. You can find it by setting F equal to C in the formula:

• C = C × 1.8 + 32
• C − 1.8C = 32
• −0.8C = 32
• C = 32 ÷ −0.8 = −40

Check it: −40 × 1.8 = −72, and −72 + 32 = −40. So −40 °C = −40 °F.

Here's why the two scales have to meet somewhere. At freezing, the Fahrenheit number starts 32 degrees higher, but Celsius degrees are bigger. As you go colder, the Celsius number falls more slowly per unit of real cooling, so the Fahrenheit number drops faster and eventually meets the Celsius number at −40. On a graph they're two straight lines with different slopes, and two such lines cross exactly once. Below −40, Fahrenheit is the lower number. Above it, Fahrenheit is the higher one.

Converting temperature changes: don't add 32

The formulas above convert a reading, such as "it's 20 °C outside." A change in temperature, such as "it got 10 °C warmer," works differently. A change only involves the size of the degree, not the starting point, so you skip the 32.

• A change in °C to a change in °F: multiply by 1.8.
• A change in °F to a change in °C: divide by 1.8.

Example: a forecast says tomorrow will be 10 °C warmer than today. That's a rise of 10 × 1.8 = 18 °F, not 50 °F. You can confirm it with real readings. 15 °C (59 °F) rising to 25 °C (77 °F) is a jump of 77 − 59 = 18 °F.

The same rule applies to tolerances, like "accurate to ±0.5 °C" (±0.9 °F), and to differences in climate data. Adding 32 to a difference is a common conversion mistake.

Where Kelvin fits in

Kelvin (K) is the SI base unit of temperature, used in science and engineering. Its zero is absolute zero, the lowest possible temperature, so a real temperature in kelvins is never negative. One kelvin is the same size as one degree Celsius, which keeps the conversion simple:

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

Examples: room temperature of 20 °C is 20 + 273.15 = 293.15 K. Absolute zero is 0 K = −273.15 °C. In Fahrenheit, that's −273.15 × 1.8 + 32 = −491.67 + 32 = −459.67 °F.

Kelvin is written without a degree sign: 300 K, not 300 °K. And because one kelvin equals one Celsius degree, a temperature change of 5 °C is also a change of 5 K.

Celsius to Fahrenheit chart for common temperatures

All values below are calculated with the exact formulas and rounded to one decimal place where needed.

Weather, home, and body temperatures

Normal body temperature varies from person to person and through the day. The 37 °C / 98.6 °F figure is a conventional reference point, not a sharp line. For questions about fever, check a medical source or ask a clinician.

Oven temperatures

Recipes rarely use exact conversions. A US recipe says 350 °F, while a UK or Australian recipe for the same dish usually says 180 °C, even though the exact match is 176.7 °C. Home ovens often drift by more than a few degrees anyway, so the rounded pairs work fine.

Cooks should know two more things. Some recipes give a separate, lower temperature for fan (convection) ovens. Lowering the temperature by about 20 °C is a common rule of thumb, but your oven's manual is the better guide. Older British recipes may also use gas marks, and gas mark conversion charts differ slightly from one source to another.

Quick reference

• Celsius to Fahrenheit: F = C × 1.8 + 32. Multiply first, then add.
• Fahrenheit to Celsius: C = (F − 32) ÷ 1.8. Subtract first, then divide.
• Mental estimate: double and add 30. It's exact at 10 °C and off by 2 °F for every 10 °C away from that. Fine for weather, not for baking.
• Reverse estimate: subtract 30 and halve. It's exact at 50 °F and off by about 1 °C for every 18 °F away from that.
• Exact mental method: double, subtract 10%, add 32.
• Temperature changes: multiply or divide by 1.8 only. Never add or subtract 32.
• Kelvin: K = C + 273.15, with no degree sign.
• Anchor points to remember: −40 = −40, 0 °C = 32 °F, 10 °C = 50 °F, 20 °C = 68 °F, 37 °C = 98.6 °F, 100 °C = 212 °F, 180 °C ≈ 350 °F.

Frequently Asked Questions

How do I convert Celsius to Fahrenheit in Excel or Google Sheets?

You can type the formula directly, such as =A1*9/5+32 for a Celsius value in cell A1. Both Excel and Google Sheets also have a built-in CONVERT function, so =CONVERT(A1,"C","F") gives the same result. To go the other way, use =CONVERT(A1,"F","C"), and use "K" for Kelvin.

What is 0 degrees Fahrenheit in Celsius?

0 °F is about −17.8 °C. The math is (0 − 32) × 5/9 = −160/9 ≈ −17.78. That's well below the freezing point of water, which is 32 °F or 0 °C.

Is multiplying by 1.8 the same as multiplying by 9/5?

Yes. 9 divided by 5 is exactly 1.8, so the two give identical results. Going the other way, multiplying by 5/9 is the same as dividing by 1.8. Dividing by 1.8 avoids the repeating decimal 0.5555..., so it's often easier on a calculator.

How precise should my temperature conversion be?

Match the precision to the use. For weather, the nearest whole degree is plenty. For oven settings, round to the nearest 5 or 10 degrees, since that's how ovens are usually marked. For lab or engineering work, keep the decimals, including the .15 in 273.15 when converting to Kelvin.