Temperature Converter
Convert temperature between Celsius, Fahrenheit, and Kelvin using exact affine formulas, with absolute-zero validation.
How It's Calculated
Formula
F = C \times \frac{9}{5} + 32 \qquad C = (F - 32) \times \frac{5}{9} \qquad K = C + 273.15Celsius, Fahrenheit, and Kelvin are three scales for the same physical quantity, temperature, but they disagree on both where zero falls and how big one degree is. Because of that, converting between them requires an offset as well as a scale factor (an affine formula), not just multiplying by a single conversion factor the way length or mass conversion does. This calculator converts Celsius and Fahrenheit through Kelvin's absolute scale internally, then reports the result in the requested unit. Kelvin has no negative values and no notion of 'degrees' — a Kelvin reading is written as, for example, '300 K', never '300 °K' — because it is defined as an absolute scale starting at absolute zero, the coldest physically possible temperature. Absolute zero is -273.15 °C, -459.67 °F, and 0 K; any input colder than that is physically invalid and is rejected rather than converted.
Worked Examples
Celsius to Fahrenheit: 0 °C (water's freezing point)
- Apply the formula: F = C x 9/5 + 32
- F = 0 x 9/5 + 32 = 0 + 32 = 32
- Result: 0 °C = 32 °F
Kelvin to Celsius: 0 K (absolute zero)
- Apply the formula: C = K - 273.15
- C = 0 - 273.15 = -273.15
- Result: 0 K = -273.15 °C, the coldest physically possible temperature
Frequently Asked Questions
Why does temperature conversion need an offset, not just a scale factor?
Celsius and Fahrenheit place their zero point at different physical temperatures (0 °C is water's freezing point; 0 °F is a much colder point defined historically), and their degree sizes also differ (a Celsius degree is larger than a Fahrenheit degree). A pure scale factor can only stretch or shrink a value around zero, so an additive offset (like the +32 in F = C x 9/5 + 32) is required to align the two scales' different zero points.
Why is -273.15 °C rejected as "below absolute zero" when it should convert to exactly 0 K?
It isn't rejected — -273.15 °C is exactly absolute zero and is a valid boundary input that converts to 0 K. Only values colder than that (e.g. -273.16 °C) are rejected, since no physical object can be colder than absolute zero.
Why is Kelvin written as "300 K" instead of "300 °K"?
Kelvin is an absolute temperature scale, not a scale of degrees offset from an arbitrary zero point like Celsius or Fahrenheit. By international convention (SI), Kelvin units are written without a degree symbol — "K", not "°K".
What is the one temperature where Celsius and Fahrenheit agree?
-40 degrees. Both scales read the same numeric value at -40 °C = -40 °F, which is where the two affine formulas happen to intersect.