Fahrenheit to Celsius Formula - Conversion, Steps, Examples

#Formula
TL;DR
The fahrenheit to celsius formula subtracts 32, then multiplies by 5/9. This article gives the exact factors, a conversion table, six worked examples, and the mistakes that flip the answer.
BT
Bhanzu TeamLast updated on November 4, 20268 min read

Key Points

  • The fahrenheit to celsius formula is ∘C=(∘F−32)×59^\circ\text{C} = (^\circ\text{F} - 32) \times \frac{5}{9}, and both 32 and the equivalent divisor 1.8 are exact values, not rounded approximations.

  • The 32 removes the gap between the two zero points, because water freezes at 32 degrees Fahrenheit but at 0 degrees Celsius.

  • The fraction 5/9 rescales the degree size, because the freezing-to-boiling span covers 100 Celsius degrees but 180 Fahrenheit degrees, and 100/180 reduces to 5/9.

  • Minus 40 degrees is the single temperature where both scales read the same number, which makes it the fastest way to check that a conversion is set up correctly.

  • NIST writes the conversion as division by 1.8 rather than multiplication by 5/9, and the two forms give identical results.

The Fahrenheit to Celsius Formula

To convert a Fahrenheit temperature to Celsius, subtract 32 and multiply by 5/9:

∘C=(∘F−32)×59^\circ\text{C} = (^\circ\text{F} - 32) \times \frac{5}{9}

The subtraction comes first, always. The United States National Institute of Standards and Technology writes the same conversion as a division, t/∘C=(t/∘F−32)/1.8t/^\circ\text{C} = (t/^\circ\text{F} - 32)/1.8, and marks both 32 and 1.8 as exact in its SI conversion tables.

Fahrenheit to Celsius Conversion Table

Degrees Fahrenheit

Degrees Celsius

What it is

−40,∘F-40,^\circ\text{F}

−40,∘C-40,^\circ\text{C}

The scales agree here

0,∘F0,^\circ\text{F}

−17.78,∘C-17.78,^\circ\text{C}

A cold winter day

32,∘F32,^\circ\text{F}

0,∘C0,^\circ\text{C}

Water freezes

50,∘F50,^\circ\text{F}

10,∘C10,^\circ\text{C}

Cool weather

68,∘F68,^\circ\text{F}

20,∘C20,^\circ\text{C}

Room temperature

98.6,∘F98.6,^\circ\text{F}

37,∘C37,^\circ\text{C}

Human body temperature

212,∘F212,^\circ\text{F}

100,∘C100,^\circ\text{C}

Water boils

350,∘F350,^\circ\text{F}

176.67,∘C176.67,^\circ\text{C}

A common baking temperature

Where the Fahrenheit to Celsius Formula Shows Up

Weather reporting is the obvious place, but the conversion carries real stakes in cooking and medicine. A recipe calling for 350 degrees Fahrenheit needs roughly 177 degrees Celsius, and an oven set to 350 degrees Celsius instead would ruin the dish and possibly the kitchen.

Clinical thermometers are the other everyday case. A reading of 100.4 degrees Fahrenheit is the standard fever threshold, and it converts to exactly 38 degrees Celsius, which is why both numbers appear in medical guidance.

What the Two Scales Actually Measure

Both scales measure the same physical quantity and differ only in where they put zero and how large they make one degree. Fahrenheit puts 32 at the freezing point of water and 212 at the boiling point, a span of 180 degrees.

Celsius puts 0 at freezing and 100 at boiling, a span of 100 degrees. Converting between them therefore needs two corrections rather than one: a shift to align the zero points, and a stretch to match the degree sizes.

Where the 32 and the 5/9 Come From

The 32 is the zero-point offset. Fahrenheit's scale was already in use when Celsius proposed his, and the freezing point of water happened to sit at 32 on it, so subtracting 32 moves a Fahrenheit reading onto a scale that starts at freezing.

The 5/9 is the degree-size ratio. Between freezing and boiling there are 100 Celsius degrees and 180 Fahrenheit degrees, so one Fahrenheit degree is 100/180 of a Celsius degree, and 100/180 reduces to 5/9.

That is also why 1.8 appears in the NIST version: 180/100 equals 1.8, and dividing by 1.8 is the same operation as multiplying by 5/9.

How to Convert Fahrenheit to Celsius

Work the two corrections in order, offset first and scale second.

Step 1. Subtract 32 from the Fahrenheit reading.

Step 2. Multiply the result by 5, then divide by 9, or divide by 1.8 to do the same job in one keystroke.

Step 3. Round only at the end, and only to the precision the situation needs.

A second route suits mental arithmetic: subtract 30 and halve. For 68 degrees Fahrenheit that gives 19, against a true 20, so it is close enough for deciding on a jacket and not close enough for a lab report.

Examples of the Fahrenheit to Celsius Formula

Example 1

Convert 50 degrees Fahrenheit to Celsius.

∘C=(50−32)×59=18×59=10^\circ\text{C} = (50 - 32) \times \frac{5}{9} = 18 \times \frac{5}{9} = 10

Final answer: 50,∘F=10,∘C50,^\circ\text{F} = 10,^\circ\text{C}

Example 2

Convert 98.6 degrees Fahrenheit to Celsius, scaling before subtracting.

The intuitive move is to reach for the 5/9 first, since it looks like the substantial part of the formula. Try it:

98.6×59=54.78,54.78−32=22.7898.6 \times \frac{5}{9} = 54.78, \qquad 54.78 - 32 = 22.78

That gives 22.78 degrees Celsius, which is room temperature. A living person is not at room temperature, so the answer is wrong before any arithmetic is checked.

The offset has to go first, because the 32 belongs to the Fahrenheit scale. Once the reading is scaled, the 32 is no longer measured in Fahrenheit degrees and subtracting it removes the wrong amount.

∘C=(98.6−32)×59=66.6×59=37^\circ\text{C} = (98.6 - 32) \times \frac{5}{9} = 66.6 \times \frac{5}{9} = 37

Final answer: 98.6,∘F=37,∘C98.6,^\circ\text{F} = 37,^\circ\text{C}

Example 3

Convert 0 degrees Fahrenheit to Celsius.

∘C=(0−32)×59=−32×59=−17.78^\circ\text{C} = (0 - 32) \times \frac{5}{9} = -32 \times \frac{5}{9} = -17.78

Final answer: 0,∘F≈−17.78,∘C0,^\circ\text{F} \approx -17.78,^\circ\text{C}

The negative sign survives the multiplication, which is the whole point of keeping the subtraction in brackets.

Example 4

Convert 350 degrees Fahrenheit to Celsius for an oven setting.

∘C=(350−32)÷1.8=318÷1.8=176.67^\circ\text{C} = (350 - 32) \div 1.8 = 318 \div 1.8 = 176.67

Final answer: 350,∘F≈176.67,∘C350,^\circ\text{F} \approx 176.67,^\circ\text{C}, set the dial to 180.

Ovens have coarse dials, so this is a case where rounding up to the nearest achievable setting beats carrying decimals.

Example 5

A thermometer reads 100.4 degrees Fahrenheit. Is that a fever by the 38 degrees Celsius standard?

∘C=(100.4−32)×59=68.4×59=38^\circ\text{C} = (100.4 - 32) \times \frac{5}{9} = 68.4 \times \frac{5}{9} = 38

Final answer: Exactly 38,∘C38,^\circ\text{C}, so the reading sits right on the threshold.

Example 6

Find the temperature at which the Fahrenheit and Celsius readings are the same number.

Set the two equal and solve. Let xx be the shared reading:

x=(x−32)×59x = (x - 32) \times \frac{5}{9} 9x=5x−1609x = 5x - 160 4x=−1604x = -160 x=−40x = -40

Final answer: −40,∘F=−40,∘C-40,^\circ\text{F} = -40,^\circ\text{C}

This is the one number worth committing to memory, because it checks any conversion in a second.

Fahrenheit to Celsius, Where Intuition Breaks

Mistake 1: Scaling before subtracting

Where it slips in: The 5/9 looks like the important operation and the 32 looks like a minor adjustment, so the hand reaches for the multiplication first.

Don't do this: 98.6×59−3298.6 \times \frac{5}{9} - 32

The correct way: (98.6−32)×59(98.6 - 32) \times \frac{5}{9}. The bracket is doing real work, not decorating the formula.

Students who have just finished a unit on order of operations are the ones who get this right, because they read the brackets as an instruction rather than as punctuation.

Mistake 2: Using 9/5 instead of 5/9

Where it slips in: The two temperature conversions are mirror images, and the fractions are easy to swap when both formulas are being revised together.

Don't do this: (68−32)×95=64.8(68 - 32) \times \frac{9}{5} = 64.8

The correct way: (68−32)×59=20(68 - 32) \times \frac{5}{9} = 20. Going from Fahrenheit to Celsius makes the number smaller, so the fraction must be less than 1.

The sense-check here is quicker than the arithmetic: Celsius numbers are smaller than Fahrenheit numbers for any everyday temperature, so an answer larger than the input is wrong on sight. The habit of glancing at the direction of change before trusting a result is what stops this one, and it is the single most useful reflex in any unit conversion.

Mistake 3: Typing the formula into a calculator without brackets

Where it slips in: A phone calculator applies order of operations strictly, so the subtraction has to be enclosed or it happens last.

Don't do this: (68−32)×5/9(68 - 32) \times 5 / 9, which the calculator reads as 68−32×5968 - \frac{32 \times 5}{9} and returns 50.2.

The correct way: (68−32)×5/9(68 - 32) \times 5 / 9, which returns 20.

Key Takeaways

  • The fahrenheit to celsius formula is ∘C=(∘F−32)×59^\circ\text{C} = (^\circ\text{F} - 32) \times \frac{5}{9}, with the subtraction always performed first.

  • The 32 corrects the different zero points and the 5/9 corrects the different degree sizes, so the formula is two separate fixes rather than one.

  • Dividing by 1.8 is identical to multiplying by 5/9, and both factors are exact rather than rounded.

  • Scaling before subtracting, or swapping 5/9 for 9/5, accounts for nearly every wrong answer, and both are caught by checking whether the number moved in the right direction.

  • To work through temperature conversion with a teacher, explore math classes online or a middle school math tutor.

Practice These Three Before Moving On

Convert 86 degrees Fahrenheit, then minus 4 degrees Fahrenheit, then 451 degrees Fahrenheit to Celsius. Check each one by converting your answer back the other way and confirming you land on the number you started with.

Want a live Bhanzu trainer to walk through more temperature conversion problems? Book a free demo class.

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Frequently Asked Questions

What is the fahrenheit to celsius formula?
∘C=(∘F−32)×59^\circ\text{C} = (^\circ\text{F} - 32) \times \frac{5}{9}. Subtract 32 first, then multiply by 5/9.
Is the fahrenheit to celsius formula exact or approximate?
Exact. NIST marks both the 32 and the 1.8 divisor as exact values, so the only approximation in any answer comes from rounding the final decimal.
Can I divide by 1.8 instead of multiplying by 5/9?
Yes. The two are the same operation written differently, since 9/5 equals 1.8. NIST's own tables use the division form.
Why do I subtract 32 before multiplying?
Because the 32 is measured in Fahrenheit degrees, and once you have multiplied by 5/9 the number is in Celsius degrees. Subtracting 32 Fahrenheit degrees from a Celsius value takes away the wrong quantity, which is what the bracket prevents.
At what temperature do Fahrenheit and Celsius read the same?
At minus 40. Both scales give minus 40 for the same physical temperature, and nowhere else do they agree.
What is 100 degrees Fahrenheit in Celsius?
About 37.78 degrees Celsius, from (100−32)×59(100 - 32) \times \frac{5}{9}.
✍️ Written By
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Bhanzu Team
Content Creator and Editor
Bhanzu’s editorial team, known as Team Bhanzu, is made up of experienced educators, curriculum experts, content strategists, and fact-checkers dedicated to making math simple and engaging for learners worldwide. Every article and resource is carefully researched, thoughtfully structured, and rigorously reviewed to ensure accuracy, clarity, and real-world relevance. We understand that building strong math foundations can raise questions for students and parents alike. That’s why Team Bhanzu focuses on delivering practical insights, concept-driven explanations, and trustworthy guidance-empowering learners to develop confidence, speed, and a lifelong love for mathematics.
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