# 4.1 Celsius and Fahrenheit formulas

The following formulas can be used to convert between Celsius and Fahrenheit.

To convert Celsius to Fahrenheit use the formula:

*F*=*C*+ 32Method:

- divide the Celsius figure by 5
- multiply by 9
- add 32.

If you prefer, you can multiply the Celsius figure by 9 first and then divide by 5. You will still need to add on 32 at the end.

To convert Fahrenheit to Celsius use the formula:

*C*=Method:

- subtract 32 from the Fahrenheit figure
- multiply by 5
- divide by 9.

If you need a recap on the rules for using formulas, revisit Session 1 ‘Working with numbers’. We will now look at an example.

## Example: Which city is warmer?

I look up the average temperature for New York on a particular day and it is 10°C. I know the average temperature in Swansea on the same day is 55°F. Which city is warmer?

You either need to convert New York’s temperature into °F or the Swansea temperature into °C.

**Method 1 – Converting °C to °F**

If we look back at the formulas above, the one we need to use to convert from °C to °F is:

*F* = *C* + 32

We need to substitute the C with our °C figure of 10°C. We then need to follow the rules of BIDMAS to carry out the calculation in stages, as shown below:

*F* = × 10 + 32

Divide the celsius figure by 5:

10 ÷ 5 = 2

Multiply by 9:

2 × 9 = 18

Add 32:

18 + 32 =

**50°F**

You may have done the calculation slightly differently by multiplying the Celsius figure by 9 first and then dividing by 5. The answer will work out the same:

*F* = × 10 + 32

Multiply by the Celsius figure by 9:

10 × 9 = 90

Divide by 5:

90 ÷ 5 = 18

Add 32:

18 + 32 =

**50°F**

So which is warmer:

New York at 10°C (which we now know is 50°F) or Swansea at 55°F?

Swansea is warmer.

**Method 2 – Converting °F to °C**

The formula for converting from °F to °C:

*C* =

We need to substitute the F with our °F figure of 55°F. We then need to follow the rules of BIDMAS to carry out the calculation in stages, as shown below:

Take 32 away from the Fahrenheit figure of 55:

- 55 − 32 = 23

Multiply by 5:

- 23 × 5 = 115

Divide by 9:

- 115 ÷ 9 =
**12.8°C**(rounded to 1 decimal place)

So which is warmer:

- New York at 10°C or Swansea at 55°F (which we now know is 12.8°C)? Swansea is warmer.

**Hint**: Google has its own unit converter (search for Google Unit Converter) which you can use to convert between various units of measure, including between °C and °F. You could try using it to double-check your answers to the questions below.

## Activity 9: Temperature conversions

Work out the answers to the following without using a calculator. You may double-check your answers on a calculator or using the Google unit converter, if needed, and remember to check your answers with ours at the end. Round your answers off to one decimal place where needed.

Convert the following temperatures into degrees Fahrenheit (°F):

- a.22°C
- b.0°C
- c.−6°C

### Answer

You need to use the following formula:

*F*=*C*+ 32a.

*F*= × 22 + 3222 ÷ 5 = 4.4

4.4 × 9 = 39.6

39.6 + 32 =

**71.6°F**b.

*F*= × 0 + 320 ÷ 5 = 0

0 × 9 = 0

0 + 32 =

**32°F**c.

*F*= × −6 + 32−6 ÷ 5 = −1.2

−1.2 × 9 = −10.8

−10.8 + 32 =

**21.2°F**

Convert the following temperatures into degrees Celsius (°C):

a.45°F

b.212°F

c.5°F

### Answer

You need to use the following formula:

*C*=a.

*C*=45 − 32 = 13

13 × 5 = 65

65 ÷ 9 =

**7.2°C**(to one d.p)b.

*C*=212 − 32 = 180

180 × 5 = 900

900 ÷ 9 =

**100°C**c.

*C*=5 − 32 = −27

−27 × 5 = −135

−135 ÷ 9 =

**−15°C**

I find a recipe which states that my oven needs to be set at a temperature of 400°F. My settings on my oven are in °C. What temperature should I set my oven to?

### Answer

You need to convert 400°F to °C so use the formula:

*C*=*C*=400 − 32 = 368

368 × 5 = 1840

1840 ÷ 9 =

**204.4°C**(to one d.p).As you would be unable to set an oven so accurately, you would set the temperature to 200°C.

- I see Moscow’s temperature is −4°C on a particular day in February, whilst the temperature in Toronto is 19°F. Which place is colder?

### Answer

You either need to convert the Moscow temperature of −4°C to °F, or convert the Toronto temperature of 19°F to °C.

**Method 1 – Converting °C to °F**If we look back at the formulas, the one we need to use to convert from °C to °F is:

*F*=*C*+ 32

We need to substitute the C with our °C figure of −4°C. We then need to follow the rules of BIDMAS to carry out the calculation in stages, as shown below:

*F*= × −4 + 32- −4 ÷ 5 = −0.8

Multiply by 9:

- −0.8 × 9 = −7.2

Add 32:

- −7.2 + 32 =
**24.8°F**

So which is colder? Moscow at −4°C (which we now know is 24.8°F) or Toronto at 19°F? Toronto is colder.

**Method 2 – Converting °F to °C**The formula for converting from °F to °C is:

*C*=

We need to substitute the F with our °F figure of 19°F. We then need to follow the rules of BIDMAS to carry out the calculation in stages, as shown below:

*C*=

Take 32 away from the Fahrenheit figure of 19:

- 19 − 32 = −13

Multiply by 5:

- −13 × 5 = −65

Divide by 9:

- −65 ÷ 9 =
**−7.2°C**(to one d.p.)

So which is colder: Moscow at −4°C or Toronto at 19°F (which we now know is −7.2°C)? Toronto is colder.

Hopefully you will be feeling more confident when solving problems relating to temperature. The next section will cover reading measurements on scales.

## Summary

In this section you have:

- practised converting between degrees Celsius (°C) and degrees Fahrenheit (°F).