Temperature Converter

Temperature Conversion Formulas

Celsius to Fahrenheit:

°F = (°C × 9/5) + 32

Fahrenheit to Celsius:

°C = (°F - 32) × 5/9

Celsius to Kelvin:

K = °C + 273.15

Kelvin to Celsius:

°C = K - 273.15

Fahrenheit to Kelvin:

K = (°F + 459.67) × 5/9

Key Reference Points

What Are the Temperature Scales?

Three scales dominate everyday and scientific life. Celsius (°C), used worldwide, sets water’s freezing point at 0° and boiling at 100°. Fahrenheit (°F), used mainly in the United States, puts those same points at 32° and 212°. Kelvin (K), the scientific absolute scale, starts at absolute zero — the coldest temperature physically possible — and uses the same degree size as Celsius. The scales differ in two ways: where zero sits (their offset) and how large each degree is (a Fahrenheit degree is 5/9 the size of a Celsius degree). Converting therefore always involves two moves: shift by the offset, then scale by the degree ratio — in either order, provided each step is done correctly.

The Rankine Scale

Engineers in some American industries use a fourth scale: Rankine (°R), the absolute version of Fahrenheit — same degree size, but starting at absolute zero. Convert with °R = °F + 459.67, so water freezes at 491.67°R and boils at 671.67°R.

Step-by-Step Conversion

Step 1: Identify your starting scale and your target scale before touching any numbers.

Step 2: Handle the Fahrenheit offset: subtract 32 when leaving Fahrenheit; you will add 32 at the end when entering it.

Step 3: Apply the degree-size ratio: multiply by 9/5 when heading toward Fahrenheit, by 5/9 when heading away from it.

Step 4: For Kelvin, just add or subtract 273.15 — Celsius and Kelvin share the same degree size, so no ratio is needed.

Step 5: Verify against a known point: 0°C must give 32°F and 273.15 K; 100°C must give 212°F.

Step 6: Respect the sign. Negative inputs are perfectly fine — and note that −40°F equals −40°C, the single point where the two scales agree.

Worked Examples

Example 1: Celsius to Fahrenheit

25°C → °F: (25 × 9/5) + 32 = 45 + 32 = 77°F — a pleasantly warm room.

Example 2: Fahrenheit to Celsius

98.6°F → °C: (98.6 − 32) × 5/9 = 66.6 × 5/9 = 37°C — normal human body temperature.

Example 3: The crossover point

−40°F → °C: (−40 − 32) × 5/9 = −72 × 5/9 = −40°C. The scales meet here and only here.

Example 4: Fahrenheit to Kelvin in two hops

212°F → K: first to Celsius, (212 − 32) × 5/9 = 100°C, then add 273.15 → 373.15 K, the boiling point of water.

Common Mistakes

• Wrong order of operations: with 25°C, multiply by 9/5 first and add 32 after. Adding 32 before multiplying is the single most common conversion error.
• Flipped ratio: 9/5 grows the number (heading toward Fahrenheit); 5/9 shrinks it (heading away). Pick by direction.
• Writing “°K”: the Kelvin unit takes no degree symbol — it is simply K.
• Impossible results: nothing can sit below −273.15°C, −459.67°F, or 0 K. A colder answer means an arithmetic slip.

Frequently Asked Questions

Why does the US still use Fahrenheit? Mostly historical inertia — its finer degrees were convenient before digital thermometers, and the cost of switching never seemed worth it.

Which scale do scientists use? Kelvin for calculations, since formulas require an absolute zero, and Celsius for everyday reporting.

Is −40 really the same in °C and °F? Yes. Setting both scales equal in °C = (°F − 32) × 5/9 solves to −40 — the unique fixed point.

Can temperature drop below absolute zero? In the ordinary sense, no: 0 K is the theoretical minimum, the point where molecular motion stops.

Readings vs Changes: The #1 Mixup

Converting a single temperature reading and converting a temperature change (ΔT) are not the same math — and mixing them up is the most common error in heat and calorimetry problems. Absolute conversions need an offset because the scales start at different zero points. A change in temperature never uses an offset, only a scale factor, because a change is a size, not a position on the scale.

Worked Example: Heating a Pot

A pot of water is heated from 20°C to 100°C. What is the change in Fahrenheit-sized degrees? The change is ΔT(°C) = 100 − 20 = 80°C, so ΔT(°F) = 80 × 9/5 = 144°F of change. Check: 212°F − 68°F = 144°F. If you had mistakenly added 32, you would get 176°F — wrong by exactly the offset.

Worked Example: A Temperature Swing

A weather station records a 100°F drop overnight. In Celsius-sized degrees that is ΔT(°C) = 100 × 5/9 ≈ 55.6°C of change — only the 5/9 scale factor appears, no offset anywhere.

Historical Scales

Celsius, Fahrenheit, Kelvin, and Rankine cover every practical need, but older scales still appear in historical texts and some recipes: Réaumur (°Ré = °C × 4/5, widely used in 18th- and 19th-century Europe), Rømer (the 1701 Danish scale that inspired Fahrenheit), Delisle (runs backwards — larger numbers mean colder), and Newton (Isaac Newton's own attempt). The Planck temperature (≈ 1.417 × 10³² K) is the natural unit of temperature in fundamental physics, where known theories stop making predictions.