# Conversion of Temperature

## Quick Celsius ( |

°C to °F | Divide by 5, then multiply by 9, then add 32 |

°F to °C | Deduct 32, then multiply by 5, then divide by 9 |

## Typical Temperatures

°C | °F | Description | |
---|---|---|---|

180 | 356 | Moderate Oven | |

100 | 212 | Water boils | |

40 | 104 | Hot Bath | |

37 | 98.6 | Body temperature | |

30 | 86 | Beach weather | |

21 | 70 | Room temperature | |

10 | 50 | Cool Day | |

0 | 32 | Freezing point of water | |

−18 | 0 | Very Cold Day | |

−40 | −40 | Extremely Cold Day (and the same number!) | |

(bold are exact) |

*16 is about 6128 is about 82*

## Explanation

There are two main temperature scales:

**°C**, the**Celsius Scale**(part of the Metric System, used in most countries)**°F**, the**Fahrenheit Scale**(used in the US), and

They both measure the same thing (temperature!), but use different numbers:

- Boiling water (at normal pressure) measures
**100° in Celsius, but 212° in Fahrenheit** - And as water freezes it measures
**0° in Celsius, but 32° in Fahrenheit**

Like this:

Looking at the diagram, notice:

- The scales start at a different number (0 vs 32), so we will need to add or subtract 32
- The scales rise at a different rate (100 vs 180), so we will also need to multiply

And so, to convert:

\frac{180}{100} can be simplified to **\frac{9}{5}**, and \frac{100}{180} can be simplified to **\frac{5}{9}**, so this is the easiest way:

**°C to °F:** Divide by 5, then multiply by 9, then add 32

**°F to °C:** Subtract 32, then multiply by 5, then divide by 9

### Example: Convert 25° Celsius *(a nice warm day) *to Fahrenheit

*First:* 25° / 5 = 5 *Then:* 5 × 9 = 45*Then:* 45 + 32 = **77° F**

### Example: Convert 98.6° Fahrenheit *(normal body temperature) *to Celsius

*First:* 98.6° − 32 = 66.6*Then:* 66.6 × 5 = 333*Then:* 333 / 9 = ** 37° C**

We can swap the order of divide and multiply if we want, but don't change the add or subtract. So this is also OK:

### Example: Convert 98.6° Fahrenheit to Celsius (again)

*First:* 98.6° − 32 = 66.6*Then:* 66.6 / 9 = 7.4*Then:* 7.4 × 5 = ** 37° C**

(Same answer as before, was it easier or harder this way?)

Fahrenheit to Celsius: (°F − 32) × \frac{5}{9} = °C

## Other Methods That Work

### Use 1.8 instead of 9/5

9/5 is equal to 1.8, so we can also use this method:

Fahrenheit to Celsius: (°F − 32) / 1.8 = °C

To make "×1.8" easier we can **multiply by 2 and subtract 10%**, but it only works for °C to °F:

### Example: Convert 20° Celsius *(A nice day) *to Fahrenheit

**20**x2 = 40- less 10% is 40−4 = 36
- 36+32 =
**68° F**

### Add 40, Multiply, Subtract 40

Since both scales cross at **−40°** (−40° C equals −40° F) we can:

- add 40,
- multiply by 5/9 (for °F to °C), or 9/5 (for °C to °F)
- subtract 40

Like this:

Fahrenheit to Celsius: Add 40, multiply by 5/9, then subtract 40

### Example: Convert 10° Celsius *(A cool day) *to Fahrenheit

**10**+40 = 50- 50×9/5 = 90
- 90−40 =
**50° F**

To remember 9/5 for °C to °F think *"F is greater than C, so there are more °F than °C"*

### Quick, but **Not Accurate**

Fahrenheit to Celsius: Subtract 30, then halve

Examples °C → °F:

**0° C**→ 0+30 →**30° F**(low by 2°)**10° C**→ 20+30 →**50° F**(exact!)**30° C**→ 60+30 →**90° F**(high by 4°)**180° C**→ 360+30 →**390° F**(high by 34°, not good)

Examples °F → °C:

**40° F**→ 10/2 →**5° C**(almost right)**80° F**→ 50/2 →**25° C**(low by about 2°)**120° F**→ 90/2 →**45° C**(low by about 4°)**450° F**→ 420/2 →**210° C**(low by about 22°, not good)

Footnote: Temperature is a measure of how fast an objects particles are moving.