Crayonbird
Menu

Science

How do you convert Celsius to Fahrenheit and Kelvin to Celsius?

Quick answer

To turn Celsius into Fahrenheit, multiply by 9/5 (1.8) and add 32. To turn Celsius into kelvin, add 273.15; to turn kelvin into Celsius, subtract 273.15.

Ages 11–16Secondary

In one sentence

Temperature conversion means writing the same temperature on a different scale: Celsius, Fahrenheit or kelvin, using a simple formula for each change.

Explained

A temperature is always the same physical thing, how hot or cold something is (see heat and temperature), but there are three scales in common use:

  • Celsius (°C) is used for weather and everyday life in most countries, and in science. Water freezes at 0 °C and boils at 100 °C.
  • Fahrenheit (°F) is used for weather, cooking and body temperature in the United States. Water freezes at 32 °F and boils at 212 °F.
  • Kelvin (K) is the SI unit used in science. It starts at absolute zero, the coldest possible temperature, so it has no negative values.
  • sun
  • snow
  • fire
Snow, a sunny day and a flame: the same temperatures can be written in °C, °F or K.

Celsius to Fahrenheit: between freezing and boiling there are 100 Celsius degrees but 180 Fahrenheit degrees (212 − 32). So each Celsius degree is 180 ÷ 100 = 1.8, or 9/5, Fahrenheit degrees. The Fahrenheit scale also starts 32 degrees higher. That gives the formulas:

°F = °C × 9/5 + 32 (or °C × 1.8 + 32)

°C = (°F − 32) × 5/9 (or (°F − 32) ÷ 1.8)

Notice the order. Going to Fahrenheit, you multiply first and then add 32. Coming back, you subtract 32 first and then divide by 1.8. These are inverse operations done in reverse order, just like undoing steps when you solve equations.

Celsius and kelvin: one kelvin is exactly the same size step as one Celsius degree. Only the starting point is different: 0 K is absolute zero, which is −273.15 °C. So:

K = °C + 273.15 and °C = K − 273.15

Many textbooks and exams round this to 273. To go between kelvin and Fahrenheit, go through Celsius first.

Two more useful facts. First, a change in temperature converts differently from a temperature reading: a rise of 10 °C is a rise of 10 K, but a rise of 18 °F (multiply by 1.8, do not add 32). Second, Celsius and Fahrenheit meet at one point: −40 °C = −40 °F. Working with temperatures below zero is good practice with negative numbers.

Examples

Temperature Celsius Fahrenheit Kelvin
Absolute zero −273.15 °C −459.67 °F 0 K
Where the scales meet −40 °C −40 °F 233.15 K
Water freezes 0 °C 32 °F 273.15 K
Warm room 20 °C 68 °F 293.15 K
Human body (about) 37 °C 98.6 °F 310.15 K
Water boils (sea level) 100 °C 212 °F 373.15 K
Oven for baking 180 °C 356 °F 453.15 K

Worked example: convert 77 °F to Celsius and to kelvin. Subtract 32: 77 − 32 = 45. Multiply by 5/9: 45 × 5 ÷ 9 = 25 °C. Then add 273.15: 25 + 273.15 = 298.15 K.

Common mistakes

  • Adding 32 before multiplying. For °C → °F, multiply by 1.8 first: 10 °C is 10 × 1.8 + 32 = 50 °F, not (10 + 32) × 1.8 = 75.6.
  • Forgetting to subtract 32 first when going back. (50 − 32) ÷ 1.8 = 10 °C; 50 ÷ 1.8 − 32 is wrong.
  • Writing “degrees kelvin”. It is just kelvin, with no degree sign: 300 K.
  • Adding 32 to a temperature change. A rise of 5 °C is a rise of 9 °F, not 41 °F.

Step by step

Step by step

  1. Check the directionAre you going to Fahrenheit, to Celsius or to kelvin?
  2. Celsius → FahrenheitMultiply by 1.8 (or by 9 and divide by 5), then add 32.
  3. Fahrenheit → CelsiusSubtract 32, then divide by 1.8 (or multiply by 5 and divide by 9).
  4. Celsius ↔ kelvinAdd 273.15 to get kelvin; subtract 273.15 to get Celsius.
  5. Sense-checkUse a landmark: 0 °C = 32 °F, 100 °C = 212 °F, 0 K = −273.15 °C.

Practice questions

Converting temperatures

Try each one, then check your answer.

  1. Convert 25 °C to Fahrenheit.
    Show answer
    25 × 1.8 + 32 = 45 + 32 = 77 °F
  2. Convert 100 °C to Fahrenheit.
    Show answer
    100 × 1.8 + 32 = 212 °F
  3. Convert −10 °C to Fahrenheit.
    Show answer
    −10 × 1.8 + 32 = −18 + 32 = 14 °F
  4. Convert 212 °F to Celsius.
    Show answer
    (212 − 32) ÷ 1.8 = 180 ÷ 1.8 = 100 °C
  5. Convert 50 °F to Celsius.
    Show answer
    (50 − 32) ÷ 1.8 = 18 ÷ 1.8 = 10 °C
  6. Convert 98.6 °F to Celsius.
    Show answer
    (98.6 − 32) ÷ 1.8 = 66.6 ÷ 1.8 = 37 °C
  7. Convert 0 °F to Celsius.
    Show answer
    (0 − 32) ÷ 1.8 = −17.8 °C (to 1 decimal place)
  8. Convert 20 °C to kelvin.
    Show answer
    20 + 273.15 = 293.15 K
  9. Convert 300 K to Celsius.
    Show answer
    300 − 273.15 = 26.85 °C
  10. Convert 0 K to Celsius.
    Show answer
    0 − 273.15 = −273.15 °C
  11. Liquid nitrogen boils at about −196 °C. What is that in kelvin?
    Show answer
    −196 + 273.15 = 77.15 K
  12. An oven is set to 180 °C. What is that in Fahrenheit?
    Show answer
    180 × 1.8 + 32 = 324 + 32 = 356 °F
  13. Convert 1 °C to Fahrenheit.
    Show answer
    1 × 1.8 + 32 = 33.8 °F
  14. At what temperature do the Celsius and Fahrenheit scales show the same number?
    Show answer
    x = 1.8x + 32 gives −0.8x = 32, so x = −40 (−40 °C = −40 °F)
  15. Convert 373.15 K to Fahrenheit.
    Show answer
    373.15 − 273.15 = 100 °C; 100 × 1.8 + 32 = 212 °F
  16. Convert −40 °F to kelvin.
    Show answer
    −40 °F = −40 °C; −40 + 273.15 = 233.15 K

Word problems

Temperatures in real life

Try each one, then check your answer.

  1. A thermometer in New York shows 86 °F. What is that in Celsius?
    Show answer
    (86 − 32) ÷ 1.8 = 54 ÷ 1.8 = 30 °C
  2. A recipe says to bake at 350 °F. What is that in Celsius?
    Show answer
    (350 − 32) ÷ 1.8 = 318 ÷ 1.8 ≈ 176.7 °C (recipes usually round this to 180 °C)
  3. The temperature rises from 15 °C to 25 °C. How big is the rise in kelvin and in Fahrenheit?
    Show answer
    10 °C = 10 K = 10 × 1.8 = 18 °F
  4. A hot summer day reaches 40 °C. What is that in Fahrenheit?
    Show answer
    40 × 1.8 + 32 = 72 + 32 = 104 °F
  5. The surface of the Sun is about 5,800 K. Roughly what is that in Celsius?
    Show answer
    5,800 − 273.15 = 5,526.85 °C, about 5,500 °C

Questions people ask

What is the formula for Celsius to Fahrenheit?

°F = °C × 9/5 + 32, which is the same as °C × 1.8 + 32. For example, 20 °C × 1.8 = 36, and 36 + 32 = 68 °F.

What is the formula for kelvin to Celsius?

°C = K − 273.15. For example, 300 K − 273.15 = 26.85 °C. Going the other way, K = °C + 273.15.

Is there a quick way to estimate Celsius to Fahrenheit?

Double the Celsius temperature and add 30. For 20 °C that gives 70 °F (the exact answer is 68 °F). To go back, subtract 30 and halve. It is close for everyday weather but not for exact work.

What is 1 °C in Fahrenheit, and what is 1 K in Celsius?

1 °C = 1 × 1.8 + 32 = 33.8 °F. 1 K = 1 − 273.15 = −272.15 °C, just above absolute zero. But a change of 1 K is the same as a change of 1 °C.

Why is kelvin written without a degree sign?

Kelvin is an absolute scale that starts at absolute zero, and its unit is simply called the kelvin, like the metre or the second. Since 1967 the official way to write it has been K, not °K.

What are common oven temperatures in Fahrenheit?

180 °C is 356 °F, usually rounded to 350 °F in recipes. 200 °C is 392 °F (about 400 °F) and 220 °C is 428 °F (about 425 °F).

How do you write the conversion in a program (C or Python)?

Use the same formula: f = c * 9 / 5 + 32. In C, take care with (9 / 5) * c: with whole numbers 9 / 5 gives 1, so write 9.0 / 5.0 instead.

Quick quiz

Temperature conversion (Celsius, Fahrenheit, Kelvin)

Check what you know with 5 quick questions.

Question 1 of 5

At what temperature does water freeze on the Fahrenheit scale?

Practise it

Try it

Practise heat and temperature with unlimited questions

Physics worksheets

See more in the library

All Physics sheets

Practise it step by step in a full course: Grade 9 Science

For grown-ups

More in Science

Heat and temperature

Temperature tells you how hot or cold something is. Heat is energy that flows from a hotter thing to a cooler one. They are linked, but they are not the same.

Science · Ages 7–13

Negative numbers

Negative numbers are numbers less than zero, written with a minus sign, like −3. You meet them in cold temperatures, bank overdrafts and floors below ground.

Maths · Ages 8–14

Melting and freezing

Melting is when a solid turns into a liquid as it heats up. Freezing is when a liquid turns into a solid as it cools. Water melts and freezes at 0 degrees Celsius.

Science · Ages 6–11

Equations

An equation says two things are equal, using an = sign, like 2x + 1 = 9. Solving it means finding the value of the letter that makes it true, here x = 4.

Maths · Ages 10–16

Acceleration

Acceleration is how quickly velocity changes. a = (v − u) ÷ t, the change in velocity divided by the time taken, measured in metres per second squared (m/s²).

Science · Ages 13–16

Density

Density is how much mass is packed into a volume. The formula is density = mass ÷ volume (ρ = m/V), measured in g/cm³ or kg/m³. Water's density is about 1 g/cm³.

Science · Ages 11–16

Back to the Learning Wiki