Celsius to Fahrenheit Calculator
Convert between Celsius and Fahrenheit — bidirectional, exact, no rounding. Water freezes at 0 °C = 32 °F and boils at 100 °C = 212 °F.
100 °C =
212
°F = °C × 9/5 + 32 → 100 × 9/5 + 32 = 212 °F. Defined exactly by NIST SP 811 §B.8 — the Celsius and Fahrenheit scales meet at −40°, and the conversion is a linear affine map with no rounding.
How to use this calculator
Type a value, pick "Celsius → Fahrenheit" or "Fahrenheit → Celsius" in the Direction select, and the result updates instantly. Flip direction to invert the conversion.
How the calculation works
The relationship is affine (linear with an offset), not a simple ratio. NIST SP 811 §B.8 defines °F = °C × 9/5 + 32 exactly. Solving for Celsius gives °C = (°F − 32) × 5/9. The two scales intersect at exactly −40° — the only temperature where the numerical values match. Because 9/5 and 32 are rational, IEEE 754 double precision preserves the round-trip within ~15 significant figures for any everyday temperature.
Worked example
Body temperature: 37 °C × 9/5 + 32 = 66.6 + 32 = 98.6 °F. Going back: (98.6 − 32) × 5/9 = 66.6 × 5/9 = 37 °C exactly. A comfortable 20 °C room = 20 × 1.8 + 32 = 68 °F. A hot summer day at 35 °C = 35 × 1.8 + 32 = 95 °F.
Frequently asked questions
What is the formula to convert Celsius to Fahrenheit?
°F = °C × 9/5 + 32, or equivalently °F = °C × 1.8 + 32. The multiplier accounts for the different degree size (1 °C is 1.8× larger than 1 °F) and the offset accounts for the different zero point (0 °C = 32 °F).
What is the formula to convert Fahrenheit to Celsius?
°C = (°F − 32) × 5/9. Subtract 32 first to remove the freezing-point offset, then multiply by 5/9 (≈ 0.5556) to rescale the degree size.
What temperature is the same in Celsius and Fahrenheit?
Exactly −40°. Setting °C × 9/5 + 32 = °C gives 4/5 × °C = −32, so °C = −40. This is the only temperature where the two scales meet — below −40, Fahrenheit is numerically higher; above −40, Celsius is.
How do I convert Celsius to Fahrenheit in my head?
Double the Celsius value and add 30 for a quick estimate. 20 °C → 20×2 + 30 = 70 °F (actual 68). 30 °C → 30×2 + 30 = 90 °F (actual 86). This shortcut is 2–5% high but good enough for weather and cooking.
Why are there two temperature scales?
Fahrenheit was defined in 1724 by Daniel Gabriel Fahrenheit around brine and body-temperature reference points. Celsius (1742) uses water freezing (0) and boiling (100). SI adopted Celsius; the US, Bahamas, Belize, Cayman Islands, and Liberia still use Fahrenheit for everyday weather.
Is the conversion factor exact?
Yes. Since 1948, the Celsius scale is defined via the kelvin (0 °C = 273.15 K exactly), and the Fahrenheit scale via °F = °C × 9/5 + 32. Both 9/5 and 32 are rational, so the conversion has no measurement uncertainty — only IEEE 754 floating-point rounding, which is ~15 significant figures.
What are the boiling and freezing points of water in both scales?
Water freezes at 0 °C = 32 °F and boils at 100 °C = 212 °F, both at standard atmospheric pressure (101.325 kPa). Body temperature is ≈ 37 °C = 98.6 °F. Room temperature is ≈ 20 °C = 68 °F.
What is absolute zero in each scale?
Absolute zero — the lowest possible temperature — is 0 K = −273.15 °C = −459.67 °F. Nothing can be colder; below this the formula still works arithmetically but has no physical meaning. This calculator returns a warning if you try it.