How to Convert Temperature Manually
Temperature is unique among common measurements: zero is not the same across scales. This means every temperature conversion requires a formula with an additive term — not just a multiplication factor. Here is every formula you need, with worked examples and a reference table.
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Why Temperature Needs a Formula (Not Just a Factor)
Most unit conversions are purely multiplicative: multiply metres by 3.28084 to get feet. Temperature is different because each scale defines its zero point differently:
- 0 °C — the freezing point of water at standard atmospheric pressure
- 0 °F — the temperature of a specific brine mixture (water, ice, ammonium chloride)
- 0 K — absolute zero; the theoretical minimum temperature
- 0 °R — also absolute zero, but on the Fahrenheit degree interval
Because the zeros differ, every conversion must first shift the zero point (via addition or subtraction) and then scale the interval (via multiplication). Kelvin and Celsius share the same interval (1 °C = 1 K), so only a shift is needed between them.
All Temperature Conversion Formulas
Celsius (°C) → Fahrenheit (°F)
°F = (°C × 9/5) + 32
Example: 25 °C → (25 × 1.8) + 32 = 45 + 32 = 77 °F
Multiply by 1.8 (= 9/5), then add 32.
Fahrenheit (°F) → Celsius (°C)
°C = (°F − 32) × 5/9
Example: 98.6 °F → (98.6 − 32) × 0.5556 = 66.6 × 0.5556 = 37.0 °C
Subtract 32 first, then multiply by 5/9 (≈ 0.5556).
Celsius (°C) → Kelvin (K)
K = °C + 273.15
Example: 25 °C → 25 + 273.15 = 298.15 K
The Kelvin scale uses the same degree size as Celsius — only the zero is shifted.
Kelvin (K) → Celsius (°C)
°C = K − 273.15
Example: 310.15 K → 310.15 − 273.15 = 37 °C
Human body temperature is 310.15 K = 37 °C = 98.6 °F.
Fahrenheit (°F) → Kelvin (K)
K = (°F − 32) × 5/9 + 273.15
Example: 32 °F → (32 − 32) × 5/9 + 273.15 = 273.15 K
Convert to Celsius as an intermediate step, then add 273.15.
Kelvin (K) → Fahrenheit (°F)
°F = (K − 273.15) × 9/5 + 32
Example: 373.15 K → (373.15 − 273.15) × 1.8 + 32 = 212 °F
Convert to Celsius first (K − 273.15), then apply the C→F formula.
Celsius (°C) → Rankine (°R)
°R = (°C + 273.15) × 9/5
Example: 0 °C → (0 + 273.15) × 1.8 = 491.67 °R
Rankine uses the Fahrenheit degree interval but starts at absolute zero.
Fahrenheit (°F) → Rankine (°R)
°R = °F + 459.67
Example: 32 °F → 32 + 459.67 = 491.67 °R
The simplest inter-scale conversion: just add 459.67.
Quick Memory Aids
- Approximate C→F: Double the Celsius value and add 30. This gives ±3 °F for everyday temperatures. Example: 20 °C → 40 + 30 = 70 °F (exact: 68 °F).
- −40 is the crossover: −40 °C = −40 °F. The two scales meet at exactly this point.
- Key landmarks: 0 °C = 32 °F (water freezes) · 37 °C = 98.6 °F (body temperature) · 100 °C = 212 °F (water boils).
- Celsius to Kelvin: Always just add 273 (or 273.15 for precision). No scale factor needed.
Temperature Reference Table
| Celsius (°C) | Fahrenheit (°F) | Kelvin (K) |
|---|---|---|
| -40 | -40 | 233.15 |
| 0 | 32 | 273.15 |
| 20 | 68 | 293.15 |
| 25 | 77 | 298.15 |
| 37 | 98.6 | 310.15 |
| 100 | 212 | 373.15 |
| 180 | 356 | 453.15 |
| -273.15 | -459.67 | 0 |
Frequently Asked Questions
What is the formula to convert Celsius to Fahrenheit?
Multiply the Celsius value by 9/5 (1.8) and then add 32. For example, 100 °C × 1.8 + 32 = 212 °F.
What is the formula to convert Fahrenheit to Celsius?
Subtract 32 from the Fahrenheit value, then multiply by 5/9. For example, (212 − 32) × 5/9 = 100 °C.
How do I convert Celsius to Kelvin?
Add 273.15 to the Celsius value. For example, 25 °C + 273.15 = 298.15 K. The Kelvin and Celsius scales share the same degree interval — only the zero point differs.
What temperature is the same in Celsius and Fahrenheit?
−40 °C equals −40 °F. This is the one point where both scales intersect.
What is absolute zero in Celsius and Fahrenheit?
Absolute zero is 0 K = −273.15 °C = −459.67 °F. It is the theoretical minimum temperature where all molecular thermal motion stops.