# Conversion of Temperature

### Quick Celsius (°C) / Fahrenheit (°F) Conversion:

Conversion Tool

Just type a value in either box:

°C:
°F:

Or use the slider, or the Interactive Thermometer,

or this method:

 °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)

## 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:

from Celsius to Fahrenheit: first multiply by 180100, then add 32
from Fahrenheit to Celsius: first subtract 32, then multiply by 100180

180100 can be simplified to 95,
and 100180 can be simplified to 59, so we get this:

°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?)

We can write them as formulas:
Celsius to Fahrenheit:   (°C × 95) + 32 = °F
Fahrenheit to Celsius:   (°F − 32) × 59 = °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:

Celsius to Fahrenheit:   °C × 1.8 + 32 = °F
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:

Celsius to Fahrenheit:   (°C × 2) less 10% + 32 = °F

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

• 20x2 = 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:

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

Like this:

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

Celsius to Fahrenheit:   Double, then add 30
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.

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