Which Is Colder: −40 °C or −40 °F?

Short answer: neither — −40 °C and −40 °F are exactly the same temperature.

Why they’re equal at −40

Celsius and Fahrenheit are both linear scales, but they use different zero points and step sizes:

Celsius (°C): 0 °C is water’s freezing point, 100 °C is its boiling point.
Fahrenheit (°F): 32 °F is freezing, 212 °F is boiling.

They’re connected by the conversion formulas:

°F = (°C × 9/5) + 32
°C = (°F − 32) × 5/9

To find where the numbers match (the same numeric value on both scales), set °F = °C = x and solve:

Start with x = (x × 9/5) + 32
Move like terms: x − (x × 9/5) = 32
Factor out x: x × (1 − 9/5) = 32
Compute the parentheses: 1 − 9/5 = 5/5 − 9/5 = −4/5
So x × (−4/5) = 32
Multiply both sides by −5/4: x = 32 × (−5/4)
Compute step-by-step: 32 ÷ 4 = 8, then 8 × (−5) = −40

Therefore, x = −40, meaning −40 °C = −40 °F.

A quick intuition

Because Fahrenheit degrees are “smaller” (you need 180 °F to cover the same boiling-to-freezing span that takes 100 °C), the Fahrenheit scale runs through numbers faster as you go colder. Starting from their different zeros (32 °F vs 0 °C) and stepping at different sizes eventually makes the two scales cross—right at −40.

Cross-checking with Kelvin (optional but neat)

Kelvin uses absolute zero as 0 K and shares Celsius’s degree size:

K = °C + 273.15

So −40 °C = 233.15 K. Converting −40 °F to Kelvin with
K = (°F + 459.67) × 5/9:

−40 + 459.67 = 419.67
419.67 × 5 = 2,098.35
2,098.35 ÷ 9 ≈ 233.15

Same result—another confirmation that −40 °C = −40 °F.

Takeaways & quick tips

At −40, the scales coincide. Neither is colder; they’re identical.
Handy landmarks:
- 0 °C = 32 °F (freezing)
- 100 °C = 212 °F (boiling)
Fast mental check: temperatures below freezing will have a lower Fahrenheit number than you might expect (because of the different zero and step size).

So the next time someone asks which is colder, you’ve got the crisp answer: neither—minus forty is minus forty, no matter the scale.