Learning goals
- Apply Celsius ↔ Fahrenheit formulas including the 32° offset
- Convert to and from Kelvin using the 273.15 shift
- Recognize when a result fails a sanity check (freezing, boiling, room temperature)
Why temperature is different
Celsius and Fahrenheit place zero at different physical points and use different degree sizes. Freezing water is 0°C but 32°F; a one-degree Celsius change is 1.8 degrees Fahrenheit.
Kelvin uses the same degree size as Celsius but starts at absolute zero. That makes K ↔ °C a simple shift: add or subtract 273.15.
Because of the offsets, you cannot convert °C to °F by multiplying by 9/5 alone — you must also add 32 (or undo that offset when going the other way).
Celsius ↔ Fahrenheit
°F = (°C × 9/5) + 32 and °C = (°F − 32) × 5/9
Scale by 9/5 (or 5/9), then apply the 32° offset. Anchors: 0°C = 32°F, 100°C = 212°F, −40°C = −40°F.
Celsius ↔ Kelvin
K = °C + 273.15 and °C = K − 273.15
Same size of degree; only the zero point moves. Room temperature near 20°C is about 293 K.
Example 1 — °C to °F
Given
Convert 37°C (typical body temperature) to Fahrenheit.
Steps
- Multiply by 9/5: 37 × 1.8 = 66.6.
- Add 32: 66.6 + 32 = 98.6.
Answer
37°C = 98.6°F.
Tip: If you forget +32 you get 66.6°F — clearly too cold for body temperature.
Example 2 — °F to °C
Given
Convert 68°F to Celsius.
Steps
- Subtract 32: 68 − 32 = 36.
- Multiply by 5/9: 36 × 5/9 = 20.
Answer
68°F = 20°C.
Example 3 — °C to Kelvin
Given
Convert −10°C to kelvin.
Steps
- Use K = °C + 273.15.
- Add 273.15: −10 + 273.15 = 263.15.
Answer
−10°C = 263.15 K.
Tip: Kelvin values for everyday weather are typically in the 250–310 K range.
Skipping the Fahrenheit offset
Common mistake
Converting 20°C → °F as 20 × 1.8 = 36°F.
Better approach
Use (°C × 9/5) + 32 → 36 + 32 = 68°F. 36°F is near freezing — a useful red flag.
Treating Kelvin like Fahrenheit
Common mistake
Applying the 9/5 and +32 path when converting to kelvin.
Better approach
Kelvin shares Celsius degree size: only add or subtract 273.15.
Check your understanding
1.Convert 0°C to Fahrenheit.
Answer: (0 × 9/5) + 32 = 32°F.
2.Convert 212°F to Celsius.
Answer: (212 − 32) × 5/9 = 100°C.
3.Convert 25°C to kelvin.
Answer: 25 + 273.15 = 298.15 K.
Key takeaways
- °C ↔ °F needs both scale (9/5) and offset (+32 or −32).
- Kelvin is Celsius shifted by 273.15 — same degree size.
- Anchor points (0°C, 100°C, −40) catch formula mistakes fast.
- Never treat temperature like a length-style single factor.