Fahrenheit to Celsius Formula Explained

The exact Fahrenheit-to-Celsius formula

The symbols mean:

• °F is the temperature in degrees Fahrenheit.
• °C is the temperature in degrees Celsius.
• 32 corrects the different zero points.
• 5/9 corrects the different degree sizes.

Both adjustments must be applied in the correct order.

Why subtract 32?

Water freezes at 32°F and 0°C under standard reference conditions. Subtracting 32 moves the Fahrenheit freezing point to zero before the scale interval is adjusted.

Without the subtraction, the conversion would incorrectly treat the two scales as though they started from the same numerical zero.

Why multiply by 5/9?

The temperature interval between water's freezing and boiling points is divided differently on the two scales.

• Fahrenheit uses 180 degrees between 32°F and 212°F.
• Celsius uses 100 degrees between 0°C and 100°C.

The ratio of the Celsius interval to the Fahrenheit interval is:

This is why the adjusted Fahrenheit value is multiplied by five-ninths.

Deriving the formula from freezing and boiling points

Start with the two common reference points:

First remove the Fahrenheit offset by subtracting 32. Then scale the remaining interval from 180 Fahrenheit divisions to 100 Celsius divisions.

Equivalent forms of the formula

The formula can be written in several mathematically equivalent forms.

Dividing by 1.8 is equivalent because 9/5 equals 1.8. The five-ninths form makes the relationship between the two degree intervals clearer.

Formula example: 77°F

Therefore, 77°F equals exactly 25°C.

Formula example: 104°F

Therefore, 104°F equals exactly 40°C.

Formula example with a repeating decimal

Some Fahrenheit temperatures do not produce whole-number Celsius results.

Convert 70°F

Rounded to two decimal places, 70°F is 21.11°C.

Formula example with a negative result

Convert 5°F

Therefore, 5°F equals exactly -15°C.

Why -40 is the same on both scales

At -40 degrees, Fahrenheit and Celsius have the same numerical value.

This crossing point occurs because the two linear scales have different offsets and different interval sizes.

Reverse formula: Celsius to Fahrenheit

The reverse conversion multiplies Celsius by 9/5 and then adds 32.

Check the reverse conversion for 20°C

Use the Celsius to Fahrenheit Converter for reverse calculations.

Exact formula versus mental estimate

The shortcut of subtracting 30 and dividing by 2 is convenient but approximate.

The approximation is useful for quick weather comparisons. Use the exact formula for body temperature, cooking, scientific work, appliance settings, or any decision where small differences matter.

Formula order of operations

Parentheses require the subtraction to be performed first:

1. Subtract 32 from Fahrenheit.
2. Multiply the result by 5.
3. Divide the result by 9.

Multiplication and division can be combined as multiplication by 5/9, but the initial subtraction must remain first.

Common formula mistakes

Using °F x 5/9 - 32

This changes the order of operations and produces an incorrect result.

Adding 32 instead of subtracting it

Adding 32 belongs to the reverse Celsius-to-Fahrenheit conversion.

Multiplying by 9/5

Nine-fifths expands Celsius degree intervals into Fahrenheit degree intervals. Fahrenheit to Celsius uses five-ninths.

Using 0.5 as the exact scale factor

Dividing by 2 can support a rough mental estimate, but the exact factor is 5/9, approximately 0.5555556.

Rounding an intermediate value

Keep the complete intermediate result and round the final Celsius value only when necessary.

The Fahrenheit to Celsius Converter applies the formula automatically.

Related Fahrenheit to Celsius guides

Frequently asked questions