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°C
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°F
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K
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°R
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°C
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°F
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K
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°R
The Temperature Conversion Calculator converts between the four major temperature scales: Celsius, Fahrenheit, Kelvin, and Rankine. Unlike most physical quantities where conversion involves simple multiplication, temperature conversions require both scaling and offset because the scales have different zero points.
The Celsius scale (°C) sets 0° at the freezing point of water and 100° at the boiling point (at 1 atm). The Fahrenheit scale (°F), used primarily in the United States, sets 32°F for freezing and 212°F for boiling. The Kelvin scale (K) is the SI thermodynamic temperature, starting at absolute zero (0 K = −273.15 °C). The Rankine scale (°R) is the Fahrenheit-based absolute scale (0 °R = absolute zero).
The core conversion formulas are:
$$°C = \frac{5}{9}(°F - 32), \qquad K = °C + 273.15$$
$$°R = °F + 459.67 = K \times \frac{9}{5}$$
Temperature is fundamentally a measure of the average kinetic energy of particles in a system. The Kelvin scale is preferred in thermodynamics and statistical mechanics because it starts at absolute zero — the point where all classical molecular motion ceases. The third law of thermodynamics states that absolute zero can be approached but never actually reached.
In everyday life, Celsius dominates most of the world's weather reports, cooking, and medical measurements. Fahrenheit persists in the US for weather and cooking. Engineering disciplines in the US sometimes use Rankine for thermodynamic calculations (e.g., in steam tables and gas turbine analysis) because it provides an absolute scale compatible with Fahrenheit degree intervals.
A particularly elegant relationship exists at −40°, where Celsius and Fahrenheit coincide: −40 °C = −40 °F. Another useful reference: body temperature is about 37 °C = 98.6 °F = 310.15 K. Room temperature is typically 20–25 °C = 68–77 °F = 293–298 K.
This calculator handles all four scales bidirectionally, normalizing through Celsius internally. Enter any temperature value, select the source scale, and read all four equivalents instantly.
The algorithm converts the input to Celsius first, then converts from Celsius to all four scales:
Step 1 — Normalize to Celsius:
$$C_{base} = \begin{cases} value & \text{from °C} \\ \frac{5}{9}(value - 32) & \text{from °F} \\ value - 273.15 & \text{from K} \\ \frac{5}{9}(value - 491.67) & \text{from °R} \end{cases}$$
Step 2 — Convert to each scale:
$$°F = C_{base} \times \frac{9}{5} + 32$$
$$K = C_{base} + 273.15$$
$$°R = (C_{base} + 273.15) \times \frac{9}{5} = K \times 1.8$$
Key reference temperatures: absolute zero = 0 K = −273.15 °C = −459.67 °F = 0 °R. Water freezes at 0 °C = 32 °F = 273.15 K. Water boils at 100 °C = 212 °F = 373.15 K. Human body temperature is 37 °C = 98.6 °F. The surface of the Sun is about 5778 K (5505 °C). Liquid nitrogen boils at 77 K (−196 °C). These reference points help build intuition for temperature values across scales.
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Water boils at 100 °C = 212 °F = 373.15 K = 671.67 °R at standard atmospheric pressure (1 atm).
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A comfortable room temperature of 72 °F equals 22.2 °C or 295.4 K — common in HVAC design and comfort standards.
Absolute zero (0 K = −273.15 °C = −459.67 °F) is the theoretical temperature at which particles have minimum possible energy. The third law of thermodynamics states it requires infinite steps (or infinite work) to reach absolute zero, making it unattainable. Scientists have cooled matter to within billionths of a kelvin above absolute zero, but never to exactly 0 K.
Historical inertia. The Fahrenheit scale was established in 1724 and became entrenched in American commerce, weather reporting, and daily life before metrication efforts began. While US science uses Kelvin and Celsius, public-facing temperature reporting, cooking, and HVAC remain in Fahrenheit. The UK uses a mixed system, with Celsius for weather but Fahrenheit still heard informally.
The Rankine scale is used primarily in US engineering thermodynamics. It provides an absolute temperature scale with the same degree size as Fahrenheit (just as Kelvin uses Celsius-sized degrees). It appears in steam tables, gas turbine analysis, and Rankine cycle calculations for power plants. Internationally, Kelvin has largely replaced Rankine.
Setting °C = °F in the conversion formula: $$C = \frac{5}{9}(C - 32) \Rightarrow 9C = 5C - 160 \Rightarrow C = -40$$. So −40 °C = −40 °F. This is the only point where the two scales intersect — a useful mnemonic and a cold day indeed (typical of Arctic or Antarctic winter).
Use: $$°F = K \times \frac{9}{5} - 459.67$$. This combines the K→°C shift (subtract 273.15) and the °C→°F conversion (multiply by 9/5, add 32) into one step. Equivalently, °F = °R − 459.67, since °R = K × 9/5.
Since 1967, the CGPM (General Conference on Weights and Measures) decided that the unit is simply "kelvin" (symbol: K) without the degree symbol (°). This reflects the fact that Kelvin is an absolute thermodynamic scale, not a relative one. We write 300 K, not 300 °K. Celsius, Fahrenheit, and Rankine retain the degree symbol because they have arbitrary zero points.
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