Celsius to Fahrenheit, Explained

Two thermometers, two numbers, and a persistent low-level confusion for anyone who travels, cooks from foreign recipes, or reads a weather forecast from the other side of the Atlantic. Converting between Celsius and Fahrenheit is not hard — but the formula is awkward enough that most people cannot do it in their head. Here is the exact method, a shortcut that gets you close in seconds, and why the two scales disagree in the first place.

The formulas

Celsius to Fahrenheit: °F = (°C × 9/5) + 32

Fahrenheit to Celsius: °C = (°F − 32) × 5/9

Two things are happening in each formula, and understanding them makes the whole thing memorable:

• The 9/5 (or 1.8) is a scaling factor. A Fahrenheit degree is smaller than a Celsius degree — there are 180 Fahrenheit degrees between freezing and boiling, but only 100 Celsius degrees. So each Celsius degree is worth 1.8 Fahrenheit degrees.
• The 32 is an offset. The two scales put their zero in different places. Water freezes at 0 °C but at 32 °F.

Because there is both a scale change and an offset, you cannot simply multiply — the order matters. Going from Celsius you multiply first, then add. Going the other way you must subtract first, then multiply. Getting that order backwards is the most common conversion mistake.

Worked example: 20 °C → (20 × 1.8) + 32 = 36 + 32 = 68 °F.

And back: 68 °F → (68 − 32) × 5/9 = 36 × 0.5556 = 20 °C. ✓

The mental shortcut

Nobody multiplies by 1.8 in their head. Use this instead:

Double it, and add 30.

For 20 °C: double to 40, add 30 → 70 °F. The true answer is 68. Close enough to know whether to bring a jacket.

Reversed: subtract 30, then halve. For 70 °F: 70 − 30 = 40, halved = 20 °C. ✓

The shortcut works because doubling approximates the 1.8 factor and 30 approximates the 32 offset. It is accurate to within a few degrees across the range of ordinary weather — which is precisely the range where you need it. It drifts further at extremes, so use the real formula for cooking or anything that matters.

Reference points worth memorising

Honestly, this is more useful than any formula for daily life. Learn a handful of anchors and you can interpolate everything between them:

• −40 °C = −40 °F — the two scales cross. A genuinely satisfying fact, and a good way to check a formula: if it does not give −40, it is wrong.
• 0 °C = 32 °F — water freezes.
• 10 °C = 50 °F — cool. A coat.
• 20 °C = 68 °F — pleasant room temperature.
• 28 °C ≈ 82 °F — properly warm.
• 37 °C = 98.6 °F — human body temperature.
• 40 °C = 104 °F — dangerously hot, whether it is the weather or a fever.
• 100 °C = 212 °F — water boils.

A neat coincidence for weather: 16 °C ≈ 61 °F and 28 °C ≈ 82 °F — the digits simply reverse. There are a few of these, and they are easier to remember than the arithmetic.

Why two scales exist at all

Fahrenheitcame first, devised by Daniel Fahrenheit in 1724. He set 0 at the coldest temperature he could reliably reproduce — a brine of ice, water and salt — and calibrated the upper end near human body temperature. The scale is anchored to human experience, which is why its defenders point out that 0–100 °F maps neatly onto “very cold” to “very hot” in ordinary weather.

Celsius arrived in 1742, and its logic is scientific rather than human: 0 and 100 are the freezing and boiling points of water. Everything is decimal, which makes it far easier to work with, and it is why virtually the entire world and all of science uses it.

Only a handful of countries still use Fahrenheit for everyday temperature — most prominently the United States. Which is why anyone reading American recipes or weather reports needs this conversion at all.

Kelvin, briefly

Science uses a third scale. Kelvin uses degrees the same size as Celsius, but starts at absolute zero — the coldest anything can theoretically be, where all thermal motion stops.

K = °C + 273.15

So 0 K is −273.15 °C. Because it has no negative values, Kelvin is what physics equations use — and note that it takes no degree symbol: it is “300 kelvin,” not “300 °K.”

Where conversion errors actually bite

• Cooking. An oven at 180 °C is 356 °F. Confuse the two and you either burn dinner or never cook it. Most recipes round to 350 °F, which is close enough for an oven.
• Fever. 38 °C is 100.4 °F — the standard fever threshold. Worth knowing in both.
• Weather when travelling.“It will be 30 today” means shorts in Celsius and a coat in Fahrenheit.
• Temperature differences. A subtle trap: if a temperature rises by 5 °C, that is a rise of 9 °F — not 41 °F. For a change in temperature you apply only the 1.8 factor, never the 32 offset. The offset applies to a point on the scale, not to a gap between two points.

Frequently asked questions

What is 100 °F in Celsius? About 37.8 °C — just above body temperature.

Is there a temperature where both scales read the same? Yes: −40. It is the only one.

Why does the US still use Fahrenheit? Largely inertia. Changing every thermostat, recipe, forecast and textbook is enormously expensive, and the current system works well enough for daily use.

Which is more accurate? Neither. They are different scales for the same physical quantity. Fahrenheit has finer degrees, so it needs fewer decimals — that is all.

Convert temperature now

Use our Temperature Converter to switch between Celsius, Fahrenheit and Kelvin instantly in your browser. For lengths, weights and volumes, try the Unit Converter.