Celsius and Fahrenheit measure the same physical quantity with different zero points and different degree sizes. Converting between them is a two-step operation: rescale the degree, then shift the zero.
This guide gives the exact formulas both ways, works through examples, provides a printable reference table, and includes mental-arithmetic shortcuts that are accurate enough for everyday use.
Convert any value instantly with the Temperature Converter.
The Conversion Formulas
Celsius to Fahrenheit
Fahrenheit to Celsius
The factor 9/5 (1.8) exists because there are 180 Fahrenheit degrees between the freezing and boiling points of water, against 100 Celsius degrees. The offset of 32 exists because water freezes at 0 °C but at 32 °F.
Order matters. Multiply before adding when going to Fahrenheit; subtract before multiplying when coming back.
Worked Example 1: Body Temperature
Worked Example 2: A Warm Day
Worked Example 3: Below Zero
Negative Celsius values do not automatically mean negative Fahrenheit values. Fahrenheit only turns negative below about −17.8 °C.
Worked Example 4: Reverse Conversion
Most recipes round this to 175 °C or 180 °C, depending on the oven's dial markings.
The Point Where the Scales Meet
−40 °C equals −40 °F exactly. It is the only value where the two readings are identical, and a useful sanity check when testing a conversion tool.
Celsius to Fahrenheit Reference Table
| Celsius | Fahrenheit | Context |
|---|---|---|
| −40 °C | −40 °F | The scales meet |
| −18 °C | 0 °F | Typical freezer setting |
| 0 °C | 32 °F | Water freezes |
| 4 °C | 39.2 °F | Refrigerator |
| 10 °C | 50 °F | Cold day |
| 16 °C | 60.8 °F | Cool room |
| 20 °C | 68 °F | Room temperature |
| 25 °C | 77 °F | Warm room |
| 30 °C | 86 °F | Hot day |
| 37 °C | 98.6 °F | Normal body temperature |
| 38 °C | 100.4 °F | Fever threshold |
| 40 °C | 104 °F | Very hot day |
| 100 °C | 212 °F | Water boils at sea level |
| 180 °C | 356 °F | Moderate oven |
| 200 °C | 392 °F | Hot oven |
| 220 °C | 428 °F | Very hot oven |
Mental Shortcuts
The double-and-add-30 rule
°F ≈ (°C × 2) + 30
For 20 °C: (20 × 2) + 30 = 70 °F. The exact value is 68 °F.
The approximation is within about 3 degrees between 0 °C and 30 °C, which covers nearly all weather conversation. It drifts badly above 40 °C, so do not use it for cooking or clinical readings.
Reverse shortcut
°C ≈ (°F − 30) ÷ 2
For 70 °F: (70 − 30) ÷ 2 = 20 °C. Exact value 21.1 °C.
Anchor points worth memorising
Learning four pairs — 0/32, 10/50, 20/68, 30/86 — lets you interpolate almost any everyday temperature without arithmetic.
Common Mistakes
- Adding 32 first. (25 + 32) × 1.8 gives 102.6 °F instead of the correct 77 °F.
- Using 5/9 in the wrong direction. The 5/9 factor belongs to Fahrenheit-to-Celsius conversion only.
- Applying the offset to a difference. A change of 10 °C is a change of 18 °F, not 50 °F. For temperature *differences*, multiply by 1.8 and do not add 32.
- Rounding too early. Round only the final answer, particularly for clinical or scientific values.
- Using the double-and-add-30 rule for oven temperatures, where it can be more than 20 degrees out.
Converting a Temperature Change
This deserves its own note because it catches people out regularly.
There is no +32, because the offset cancels when you subtract two absolute temperatures. Use the full formula for a temperature *reading*; use only the 1.8 factor for a temperature *interval*.
Where Each Scale Is Used
Fahrenheit remains in everyday use in the United States and a small number of associated territories. Celsius is the standard in the rest of the world and in scientific work everywhere, including in the United States. Kelvin is the SI base unit for thermodynamic temperature and is used in physics, chemistry and engineering.
Kelvin has no degree symbol and no negative values, because 0 K is absolute zero.
Practical Applications
Cooking. Recipes from US sources use Fahrenheit; most ovens outside the US are marked in Celsius. Convert, then round to the nearest 5 degrees your dial supports.
Weather. For clothing decisions, the double-and-add-30 rule is entirely adequate.
Health. Convert precisely. The difference between 38.0 °C (100.4 °F) and 38.5 °C (101.3 °F) matters, and a shortcut can obscure it.
Engineering and equipment ratings. Datasheets often list operating ranges in one scale only. Convert with the exact formula and keep one decimal place.
Scientific work. Convert Celsius to Kelvin before using temperature in gas-law or thermodynamic equations; those formulas require absolute temperature.
Related Tools
- Temperature Converter — Celsius, Fahrenheit, Kelvin and Rankine
- Unit Converters — length, mass, area, volume, speed and more
- Length Converter — metres, feet, inches and miles
- Energy Converter — joules, calories, kWh and BTU
- Scientific Calculator — for multi-step conversions
Frequently Asked Questions
What is the formula to convert Celsius to Fahrenheit?
°F = (°C × 9/5) + 32. Multiply by 1.8 first, then add 32.
What is 100 °C in Fahrenheit?
212 °F — the boiling point of water at standard atmospheric pressure.
Is there a temperature where Celsius and Fahrenheit are equal?
Yes, −40. It is the only point where the two scales give the same reading.
Why is normal body temperature 98.6 °F?
Because it is the conversion of 37 °C, which was itself a rounded 19th-century average. Normal body temperature actually varies by person, time of day and measurement site.
How do I convert a temperature difference rather than a reading?
Multiply the Celsius difference by 1.8. Do not add 32 — the offset cancels out when comparing two temperatures.
Summary
°F = (°C × 1.8) + 32 for readings, ×1.8 alone for differences, and the two scales meet at −40. Use the double-and-add-30 rule for casual estimates and the exact formula for anything involving health, cooking or equipment. Check your result on the Temperature Converter.