The Celsius to Fahrenheit formula
To convert a temperature from Celsius to Fahrenheit, multiply the Celsius value by 9/5 (or 1.8) and add 32:
F = C × 9/5 + 32
This is an exact linear relationship, not an approximation. It comes directly from how the two scales are defined: both are straight-line (linear) temperature scales, but they use different zero points and different degree sizes. A Celsius degree is 1.8 times larger than a Fahrenheit degree, which is why the 9/5 (or 1.8) multiplier appears, and the two scales are offset by 32 degrees at the freezing point of water, which is why 32 is added.
Why Celsius and Fahrenheit don't line up at zero
The Celsius scale, devised by Anders Celsius in 1742, sets 0°C at the freezing point of water and 100°C at its boiling point (at standard atmospheric pressure), with exactly 100 equal degrees between them. The Fahrenheit scale, created by Daniel Gabriel Fahrenheit in the early 1700s, sets water's freezing point at 32°F and its boiling point at 212°F — a span of 180 degrees for the same physical temperature range. Dividing 180 by 100 gives the 9/5 ratio between the scales, and the 32-degree offset accounts for Fahrenheit's zero point being set well below water's freezing point.
Reference points worth memorizing
A few benchmark conversions make it easy to sanity-check any result:
- Water freezes: 0°C = 32°F
- Water boils (sea level): 100°C = 212°F
- Normal human body temperature: 37°C ≈ 98.6°F
- Room temperature: 20°C = 68°F
- A hot summer day: 35°C = 95°F
- A typical baking oven: 180°C = 356°F
- The one temperature where both scales agree: −40°C = −40°F
How the calculator works
Enter a temperature in Celsius into the input field and click Calculate. The tool applies F = C × 9/5 + 32 and displays the result in Fahrenheit, rounded to two decimal places. As a bonus reference, it also shows the equivalent Kelvin value using K = C + 273.15, since Kelvin (the SI base unit for temperature) is often needed alongside Fahrenheit in scientific and engineering contexts. There are no hidden modes, weighting factors, or scenario settings — the math is a single, exact linear conversion, so the same Celsius input always produces the same Fahrenheit output.
Going the other direction
To convert Fahrenheit back to Celsius, rearrange the formula: C = (F − 32) × 5/9. For example, 98.6°F gives (98.6 − 32) × 5/9 = 37°C, confirming normal body temperature. If you need to convert Fahrenheit to Celsius directly, use our dedicated Fahrenheit to Celsius calculator, or simply subtract 32 first and then multiply by 5/9 (not 9/5) by hand.
Common mistakes when converting by hand
The most frequent error is reversing the order of operations: you must multiply by 9/5 before adding 32, not after. For example, 20°C × 9/5 = 36, then + 32 = 68°F (correct) — not 20 + 32 = 52, then × 9/5 = 93.6°F (wrong). Another common mistake is using 5/9 instead of 9/5 when converting from Celsius to Fahrenheit; remember, 5/9 is only used when converting from Fahrenheit to Celsius. Finally, for negative Celsius values, be careful with sign: −10°C × 9/5 = −18, then + 32 = 14°F.
FAQ
What is 100°C in Fahrenheit? 100°C equals 212°F, the boiling point of water at sea level.
What is 0°C in Fahrenheit? 0°C equals 32°F, the freezing point of water.
Is the Celsius-to-Fahrenheit conversion exact or approximate? It is mathematically exact. F = C × 9/5 + 32 is a defined linear relationship between the two scales, with no rounding involved except in the decimal places you choose to display.
What temperature is the same in both Celsius and Fahrenheit? −40 degrees. At −40°C the Fahrenheit value is also −40°F — this is the single point where the two linear scales intersect.
Why does the US use Fahrenheit while most other countries use Celsius? Fahrenheit was the scientific standard when the United States began standardizing measurements in the 18th and 19th centuries, and it remained in common use even after most of the world adopted the metric-based Celsius scale in the 20th century. Science, including US weather forecasting's underlying data and medicine, frequently uses Celsius or Kelvin regardless of country.
How do I convert a temperature difference (not an absolute temperature)? For a change in temperature (for example, "the temperature rose by 5°C"), multiply only by 9/5 and do not add 32, since the offset only applies to absolute readings: a 5°C increase equals a 9°F increase.