The formulas
Fahrenheit and Celsius are both relative scales with different zero points and different degree sizes. Water freezes at 32 F / 0 C and boils at 212 F / 100 C at sea level, so 180 Fahrenheit degrees span the same range as 100 Celsius degrees. That gives the conversion: F = C x 9/5 + 32, and C = (F - 32) x 5/9. The two scales cross at -40, the only temperature that reads the same in both.
Kelvin is the SI absolute scale used in science. It has the same degree size as Celsius but starts at absolute zero: K = C + 273.15, so 0 K = -273.15 C = -459.67 F, and Kelvin values are never negative (they are written without a degree sign, as 300 K). Rankine is the absolute version of Fahrenheit, used in some US engineering work: R = F + 459.67. A temperature difference of 10 C is a difference of 10 K and of 18 F.
Everyday reference points
Body temperature: 98.6 F is exactly 37 C, and the usual fever threshold of 100.4 F is 38 C. Weather: 32 F is freezing, 50 F is 10 C (light jacket), 68 F is 20 C, 86 F is 30 C (hot), and 100 F is 37.8 C. A thermostat set to 72 F is 22.2 C. The kitchen: a moderate oven at 350 F is 176.7 C (most metric recipes say 180 C), 400 F is 204 C, 425 F is 218 C, and a 450 F roast is 232 C. Food safety: keep the refrigerator at or below 40 F (4.4 C), the freezer at 0 F (-17.8 C), and cook poultry to 165 F (73.9 C).
Worked example: to convert 77 F to Celsius, subtract 32 to get 45, then multiply by 5/9 to get 25 C. To convert 30 C to Fahrenheit, multiply by 9/5 to get 54, then add 32 to get 86 F. For Kelvin, 25 C + 273.15 = 298.15 K, which is the standard reference temperature in many chemistry tables.
Quick mental math and caveats
For a rough Fahrenheit-to-Celsius estimate, subtract 30 and halve the result: 70 F becomes about 20 C (exact: 21.1 C). For Celsius to Fahrenheit, double it and add 30: 25 C becomes about 80 F (exact: 77 F). The error grows at the extremes, so use the exact formula for oven settings, medical readings and anything scientific.
Remember that the boiling point drops with altitude: water boils near 203 F (95 C) in Denver, which is why high-altitude baking instructions differ. Many digital thermometers and imported appliances can be switched between F and C in their settings; the converter shows two decimals, which is more precision than most thermometers actually deliver.