Temperature Conversion
Our free thermal & energy converter handles temperature conversion conversions. See tables, ratios, and examples for quick reference.
Temperature Conversion
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Formula: F = C x 9/5 + 32 | K = C + 273.15 | R = K x 9/5 | Re = C x 4/5
Worked example — 450 K = 176.85 C = 350.33 F = 810 R = 141.48 Re
Formula
F = C x 9/5 + 32 | K = C + 273.15 | R = K x 9/5 | Re = C x 4/5
Temperature conversion requires both scaling and offsetting because different scales have different degree sizes and zero points. Celsius-Kelvin differ only by an offset of 273.15. Fahrenheit-Rankine differ by 459.67. Between Celsius and Fahrenheit, both a scale factor (9/5) and offset (32) are needed.
Worked Examples
Example 1: Multi-Scale Scientific Conversion
Problem:A chemical reaction occurs at 450 K. Express this in all temperature scales.
Solution:Celsius: 450 - 273.15 = 176.85 degrees C Fahrenheit: 176.85 x 9/5 + 32 = 350.33 degrees F Rankine: 450 x 9/5 = 810 degrees R Reaumur: 176.85 x 4/5 = 141.48 degrees Re
Result:450 K = 176.85 C = 350.33 F = 810 R = 141.48 Re
Example 2: Engineering Temperature Conversion
Problem:Steam enters a turbine at 1,000 degrees R. Convert to Kelvin and Celsius.
Solution:Kelvin: 1,000 x 5/9 = 555.56 K Celsius: 555.56 - 273.15 = 282.41 degrees C Fahrenheit: 1,000 - 459.67 = 540.33 degrees F
Result:1,000 R = 555.56 K = 282.41 C = 540.33 F
Frequently Asked Questions
What are all the temperature scales?
The main temperature scales are Celsius (used worldwide for everyday measurement), Fahrenheit (used in the US), Kelvin (SI standard for science), Rankine (absolute scale using Fahrenheit degrees, used in some US engineering), Reaumur (historic European scale where water freezes at 0 and boils at 80), and Delisle (inverted scale, now obsolete). Celsius and Kelvin have the same degree size; Fahrenheit and Rankine have the same degree size.
How do Kelvin and Rankine scales compare?
Both Kelvin and Rankine are absolute temperature scales starting at absolute zero, but they use different degree sizes. Kelvin uses the Celsius degree size (1 K = 1 C increment), while Rankine uses the Fahrenheit degree size (1 R = 1 F increment). The conversion is: R = K x 9/5. So absolute zero is 0 K = 0 R, and water freezes at 273.15 K = 491.67 R. Rankine is primarily used in US thermodynamic engineering.
What is the Reaumur scale?
The Reaumur scale was proposed by Rene Antoine Ferchault de Reaumur in 1730. It sets water freezing at 0 degrees Re and boiling at 80 degrees Re at standard atmospheric pressure. The conversion to Celsius is straightforward: C = Re x 5/4. The Reaumur scale was widely used in Europe until the mid-20th century, particularly in France, Germany, and Russia. Today it is mostly of historical interest, though some European food recipes still reference it.
At what temperature are Celsius and Fahrenheit equal?
Celsius and Fahrenheit read the same at exactly -40 degrees. You can verify: F = (-40 x 9/5) + 32 = -72 + 32 = -40. This is the only point where both scales intersect. Above -40, Fahrenheit values are always higher than Celsius. At 0 degrees C (water freezing), Fahrenheit reads 32 degrees. The scales diverge further as temperature increases: 100 degrees C = 212 degrees F, a difference of 112 scale degrees.
Why is Kelvin used in scientific calculations?
Kelvin is used in science because it is an absolute scale with its zero at the lowest theoretically possible temperature. This makes it essential for thermodynamic equations like the ideal gas law (PV = nRT), Stefan-Boltzmann radiation law, and entropy calculations. Using Celsius in these formulas would produce wrong results because negative Celsius values do not represent negative thermal energy. Kelvin ensures proportional relationships remain mathematically valid.
How do I convert a temperature difference rather than a temperature reading?
Differences drop the offset and keep only the scale factor, because the offset cancels when you subtract two readings. A change of 1 degree Celsius is a change of exactly 1 kelvin and 1.8 degrees Fahrenheit, and a change of 1 degree Fahrenheit is a change of 1 degree Rankine. So a room that warms by 10 degrees Celsius has warmed by 18 degrees Fahrenheit, not by 50. Applying the full C times 9/5 plus 32 formula to an interval is a classic error in heat transfer and HVAC calculations.
What is absolute zero on each temperature scale?
Absolute zero is the point where classical thermal motion ceases, and it anchors the absolute scales. It sits at 0 K, which equals minus 273.15 degrees Celsius and minus 459.67 degrees Fahrenheit, and it is also 0 degrees Rankine, since Rankine is the absolute scale built on Fahrenheit sized degrees. These figures are the offsets used throughout the conversions on this page, which is why kelvin equals Celsius plus 273.15 and Rankine equals Fahrenheit plus 459.67.
How do I convert Fahrenheit to Celsius by hand?
Subtract 32 first, then multiply by 5/9: C equals (F minus 32) times 5/9. A body temperature of 98.6 F gives 66.6 multiplied by 5/9, which is 37 degrees Celsius exactly. The order matters, because multiplying before removing the offset gives a wrong answer. A rough mental version is to subtract 30 and halve, which turns 70 F into about 20 C against a true value of 21.1 C, close enough for weather but not for anything technical.
Why do the Celsius and Fahrenheit formulas use a factor of 9/5?
The factor comes from how many degrees each scale places between the same two physical fixed points. Celsius puts 0 at the freezing point of water and 100 at its boiling point at standard atmospheric pressure, spanning 100 degrees. Fahrenheit places those same two points at 32 and 212, spanning 180 degrees. The ratio 180 to 100 reduces to 9/5, so a Fahrenheit degree is a smaller increment than a Celsius degree, and the 32 in the formula accounts for the different zero points.
What is the correct way to write kelvin values compared with Celsius?
Kelvin is an SI base unit rather than a degree scale, so it takes no degree symbol and is written as 300 K, never as 300 degrees Kelvin. Celsius keeps the degree symbol and is written as 27 degrees Celsius. The unit name is lower case, kelvin, while the symbol K is capitalised after its namesake. This matters in scientific writing and in software output, where a stray degree symbol on a kelvin figure is a reliable signal that a conversion was done by hand and never checked.
References
Background & Theory
F = C x 9/5 + 32, K = C + 273.15, and R = F + 459.67 - all three relationships are exact. Temperature is the one everyday conversion that needs an offset as well as a scale factor, because the scales disagree on where zero sits.
Conversion reference table
| Conversion | Equivalent | Exact or rounded? |
|---|---|---|
| Water freezes | 0 C = 32 F = 273.15 K = 491.67 R | Exact |
| Water boils (1 atm) | 100 C = 212 F = 373.15 K = 671.67 R | Exact |
| Absolute zero | -273.15 C = -459.67 F = 0 K = 0 R | Exact by definition |
| Scales cross | -40 C = -40 F | Exact |
| 1 Celsius degree interval | 1 kelvin = 1.8 Fahrenheit degrees = 1.8 Rankine | Exact |
| Reaumur | Re = C x 4/5 | Exact - historical scale |
Rankine is to Fahrenheit what kelvin is to Celsius: an absolute scale with the same degree size, used in American thermodynamics and gas-turbine work. Keep readings and intervals apart - a reading of 20 C is 68 F, but a rise of 20 C is a rise of 36 F, because the offset applies once to a reading and not at all to a difference. Since 2019 the kelvin has been fixed by an exact value of the Boltzmann constant rather than by the triple point of water.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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