Temperature Converter
Convert Celsius, Fahrenheit, kelvin, Rankine and Réaumur readings with exact scale formulas. Switch to Temperature interval mode when you need to convert a rise, fall or difference without applying an origin offset.
- Five temperature scales
- Absolute and interval modes
- Exact rational arithmetic
- Absolute-zero validation
Convert Temperature or Temperature Difference
Enter a decimal, scientific-notation value, fraction or mixed number. Absolute temperature uses offsets and scale ratios. Temperature intervals use only scale ratios. Rounding changes the displayed result, not the stored conversion.
Temperature conversion result
32.00 degrees Fahrenheit
0 °C converted with the exact Celsius–Fahrenheit relationship.
Equivalent Temperatures
| Scale | Symbol | Equivalent value |
|---|---|---|
| degree Celsius | °C | 0 °C |
| degree Fahrenheit | °F | 32 °F |
| kelvin | K | 273.15 K |
| degree Rankine | °R | 491.67 °R |
| degree Réaumur | °Ré | 0 °Ré |
Calculation Steps
- Read 0 °C as an absolute temperature.
- Add 273.15 to obtain exactly 273.15 K.
- Confirm the normalized value is not below 0 K.
- Apply the Fahrenheit ratio and offset to obtain exactly 32 °F.
- Display 32.00 °F at 2 decimal places.
This converts one scale representation to another. It does not increase the accuracy of the original measurement.
The complete result is selected. Use your device copy command.
How to Use This Temperature Converter
Allow about two minutes to select the right mode, enter the value and review the result.
- Choose absolute temperature or interval. Use Absolute temperature for a thermometer reading. Use Temperature interval for a rise, fall, range or difference.
- Enter one value. Use a decimal such as 98.6, scientific notation such as 3e2, a fraction such as 1/2 or a mixed number such as 1 1/2. Leave out the unit symbol.
- Select the source and target scales. Choose Celsius, Fahrenheit, kelvin, Rankine or Réaumur. Kelvin uses K, not °K.
- Choose display precision. Select decimal places or significant figures, enter the required count and choose a halfway rounding rule.
- Press Convert. Review the target value, kelvin basis, all-scale equivalents, exact value and calculation steps.
- Copy, swap or reset. Copy the complete result, swap scales while preserving the exact stored value, or restore the 0 °C to 32 °F example.
Absolute mode accepts negative Celsius, Fahrenheit and Réaumur values when the normalized result is at least 0 K. It accepts exactly 0 K as the mathematical boundary. Interval mode allows positive, zero or negative differences because a negative interval describes a decrease.
Temperature Conversion Formulas
Absolute scales do not share one zero point. The converter therefore normalizes each reading through kelvin before applying the target scale. The relationships below use exact constants.
To leave kelvin, reverse the applicable relationship: °C = K − 273.15, °F = K × 9/5 − 459.67, °R = K × 9/5, and °Ré = (K − 273.15) × 4/5.
Direct Celsius and Fahrenheit formulas
The offset handles the different scale origins. It belongs to an absolute reading, not to a temperature change.
Temperature interval formulas
An interval has no scale origin. A change of 10 Celsius degrees equals 10 kelvins, 18 Fahrenheit degrees, 18 Rankine degrees or 8 Réaumur degrees. Adding 32 or 273.15 to an interval would be incorrect.
Worked Temperature Conversion Examples
Example 1: Convert 0 °C to °F
Multiply 0 by 9/5, then add 32. The exact result is 32 °F.
Example 2: Convert 98.6 °F to °C
Subtract 32, then multiply by 5/9. The difference is 66.6 °F. Multiplying by 5/9 gives exactly 37 °C.
Example 3: Convert −40 °C to °F
Multiply −40 by 9/5 and add 32. The result is −40 °F. This is the point where the Celsius and Fahrenheit scales have the same numerical value.
Example 4: Convert 300 K to °C
Subtract the exact offset 273.15. The result is exactly 26.85 °C. Converting the same reading to Fahrenheit gives exactly 80.33 °F.
Example 5: Convert a 20 °C interval to °F
Use interval mode. Multiply 20 by 9/5. The change is exactly 36 °F. Do not add 32 because the value describes a difference rather than an absolute reading.
Exact Scale Reference Values
These rows are mathematical scale equivalents. They are not claims about a material, weather condition, cooking process or fixed water phase point.
| Celsius | Fahrenheit | Kelvin | Rankine | Réaumur |
|---|---|---|---|---|
| −273.15 °C | −459.67 °F | 0 K | 0 °R | −218.52 °Ré |
| −40 °C | −40 °F | 233.15 K | 419.67 °R | −32 °Ré |
| 0 °C | 32 °F | 273.15 K | 491.67 °R | 0 °Ré |
| 20 °C | 68 °F | 293.15 K | 527.67 °R | 16 °Ré |
| 100 °C | 212 °F | 373.15 K | 671.67 °R | 80 °Ré |
The first row is the ordinary thermodynamic-temperature boundary used by this converter. A value below it is rejected in absolute mode. The tool does not decide whether an entered temperature is experimentally attainable or which practical temperature scale an instrument realizes.
Absolute Temperature Versus Temperature Difference
An absolute temperature locates a reading on a scale. A temperature difference compares two readings. The distinction changes the equation whenever Celsius, Fahrenheit or Réaumur is involved.
For example, 10 °C as an absolute temperature equals 50 °F. A rise of 10 Celsius degrees equals a rise of 18 Fahrenheit degrees. The absolute conversion includes 32 because the zero points differ. The interval conversion uses only the 9/5 scale ratio.
Kelvin and Celsius increments have the same magnitude. Rankine and Fahrenheit increments also have the same magnitude. Réaumur uses 80 degrees across the span represented by 100 Celsius degrees, so one Réaumur-degree interval equals 1.25 K.
Kelvin, Celsius and Absolute Zero
The kelvin, symbol K, is the SI unit of thermodynamic temperature. Its current definition fixes the numerical value of the Boltzmann constant. Write 300 K, not 300 °K or 300 degrees kelvin.
Celsius temperature is related to thermodynamic temperature by the exact equation t/°C = T/K − 273.15. A degree Celsius interval has the same magnitude as one kelvin. The scale relationship is exact, while a thermometer reading still has calibration, resolution and measurement uncertainty.
Zero kelvin is commonly called absolute zero. This converter accepts 0 K, −273.15 °C, −459.67 °F, 0 °R and −218.52 °Ré as equivalent boundary values. It rejects lower ordinary thermodynamic-temperature readings. It does not model specialized negative-temperature systems or convert a practical scale such as ITS-90 into an exact thermodynamic temperature.
Water phase temperatures are useful practical references, but pressure, composition and measurement conditions matter. The Celsius scale is not currently defined by assuming that water always freezes at exactly 0 °C or boils at exactly 100 °C.
Exact Formulas, Rounding and Measurement Precision
The converter stores the input and every scale constant as rational numbers. Ratios such as 5/9 remain fractions instead of shortened decimals. This prevents a repeating intermediate value from causing avoidable drift when you swap scales.
Keep these ideas separate:
- Exact scale relationship: the defined offset and ratio between scale values.
- Exact mathematical target: the entered number transformed by that relationship.
- Displayed result: the target rounded to your selected decimal places or significant figures.
- Measured temperature: a value limited by the thermometer, method, environment and calibration.
The default rule is round-to-nearest, ties-to-even. The alternate rule moves an exact halfway magnitude away from zero. The calculator shows an approximation sign only when the selected display differs from the stored exact result. It normalizes negative zero to zero.
Common Temperature Conversion Mistakes
- Adding 32 before multiplying in the wrong direction. For Fahrenheit to Celsius, subtract 32 first, then multiply by 5/9.
- Applying offsets to a change. Temperature intervals use scale ratios only.
- Writing °K. The kelvin symbol is K without a degree sign.
- Calling kelvin “degrees kelvin.” Use kelvin or kelvins.
- Confusing °R and °Ré. °R means Rankine here. °Ré marks the historical Réaumur scale.
- Accepting a reading below 0 K. Convert through kelvin and check the ordinary thermodynamic boundary.
- Rounding the 5/9 ratio early. Keep the exact fraction until the final display.
- Creating false precision. More displayed digits do not improve a thermometer measurement.
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Frequently Asked Questions
How do I convert Celsius to Fahrenheit?
Multiply the Celsius value by 9/5, then add 32. For example, 20 °C becomes 68 °F. For a Celsius temperature interval, multiply by 9/5 but do not add 32.
How do I convert Fahrenheit to Celsius?
Subtract 32 from the Fahrenheit value, then multiply by 5/9. For example, 68 °F becomes 20 °C. For a Fahrenheit interval, multiply by 5/9 without subtracting 32.
How do I convert Celsius to kelvin?
Add exactly 273.15 to the Celsius value. Thus 0 °C equals 273.15 K, while −273.15 °C equals 0 K. The kelvin symbol has no degree sign.
What is the difference between temperature and temperature interval modes?
Absolute temperature uses scale origins and ratios. An interval measures only a difference, so it uses ratios without offsets. Ten degrees Celsius is 50 °F, but a 10 Celsius-degree change equals an 18 Fahrenheit-degree change.
What is absolute zero on each supported scale?
The equivalent boundary values are 0 K, −273.15 °C, −459.67 °F, 0 °R and −218.52 °Ré. The converter accepts the boundary and rejects lower values in absolute mode.
Why is −40 the same in Celsius and Fahrenheit?
Solving °F = °C × 9/5 + 32 for equal numerical values gives −40. Therefore −40 °C equals exactly −40 °F.
Does kelvin use a degree sign?
No. Write the unit name kelvin and the symbol K, such as 300 K. Forms such as °K and “degrees kelvin” are not current SI style.
What are Rankine and Réaumur?
Rankine is an absolute scale whose degree interval matches Fahrenheit; 0 °R equals 0 K. Réaumur is a historical non-SI scale conventionally mapped so 0 °Ré equals 0 °C and 80 °Ré equals 100 °C.
Are temperature conversions exact?
The scale relationships used here are exact. A displayed decimal may be rounded, and an entered measurement still has uncertainty. Exact conversion does not improve thermometer accuracy.
Does this converter calibrate a thermometer?
No. It changes the numerical representation between scales. Calibration, sensor response, uncertainty, environmental conditions and practical temperature-scale realization require separate measurement procedures.
Calculation Method and Review Basis
- BIPM SI Brochure, 9th edition, current kelvin definition, Celsius offset, interval rules and unit style.
- BIPM Kelvin Base Unit, the fixed Boltzmann-constant definition.
- NIST SI Units of Temperature, exact Celsius, Fahrenheit and kelvin formulas.
- NIST SP 811 Appendix B.8, temperature-scale and interval conversion relationships.
- NIST Kelvin Introduction, absolute-zero and kelvin notation guidance.
- NIST Technical Note 910-8, historical Rankine and Réaumur scale conventions and symbol distinctions.
Measurement disclaimer: This converter applies mathematical scale relationships to the value you enter. It does not certify a thermometer, calibrate a sensor, determine material phase behavior, establish cooking or medical safety, or replace a laboratory, engineering, weather, industrial or legal-metrology procedure. Confirm the instrument, uncertainty, practical temperature scale, conditions and governing requirements before using a result for health, trade, laboratory, engineering, legal or safety decisions.