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Temperature Unit Converter

Convert temperature between Celsius, Fahrenheit, Kelvin, Rankine, and Réaumur scales. Useful for thermal analysis, datasheet comparison, and engineering calculations.

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Formula

F=95C+32,K=C+273.15F = \frac{9}{5}C + 32, \quad K = C + 273.15
C— Celsius (°C)
F— Fahrenheit (°F)
K— Kelvin (K)
R— Rankine (°R)
Ré— Réaumur (°Ré)

How It Works

This calculator converts between Celsius, Fahrenheit, Kelvin, Rankine, and Reaumur temperature scales for engineers, scientists, and technicians working with thermal measurements. Per SI Brochure (BIPM) and NIST SP 811, Kelvin is the SI base unit with absolute zero at exactly 0 K = -273.15 C = -459.67 F. The 2019 SI redefinition fixed the Boltzmann constant k = 1.380649 × 10^-23 J/K exactly, making temperature traceable to energy. Critical conversion: C to F uses T_F = T_C × 9/5 + 32 exactly. Electronics thermal design operates from -40 C (industrial minimum per IEC 60068) to +125 C (automotive maximum per AEC-Q100), a 165 C span. Junction temperatures in power semiconductors reach 150-175 C, requiring accurate thermal calculations with typical tolerances of +/-2 C.

Worked Example

Problem

A CPU thermal specification lists maximum T_junction = 100 C and thermal resistance theta_JA = 25 C/W. Calculate operating margins at 25 C and 85 C ambient with 3 W dissipation.

Solution
  1. At 25 C ambient: T_J = 25 + (3 × 25) = 100 C (at limit)
  2. At 85 C ambient: T_J = 85 + (3 × 25) = 160 C (exceeds 100 C limit by 60 C)
  3. Convert to Kelvin: 100 C + 273.15 = 373.15 K
  4. Convert to Fahrenheit: 100 × 9/5 + 32 = 212 F (boiling point of water)
  5. Margin at 25 C: (100 - 100)/100 = 0% - no margin, reduce power or add heatsink
  6. Required theta_JA at 85 C: (100 - 85)/3 = 5 C/W - needs 5x better cooling

Practical Tips

  • ✓Semiconductor temperature grades per JEDEC/AEC: Commercial 0 to +70 C, Industrial -40 to +85 C, Automotive -40 to +125 C (AEC-Q100), Military -55 to +125 C (MIL-STD-883). Always match component grade to operating environment
  • ✓Thermal noise power = kTB where k = 1.380649 × 10^-23 J/K (exact SI), T in Kelvin, B in Hz. At 290 K (17 C), noise power density = -174 dBm/Hz - this defines receiver sensitivity limits
  • ✓Per NIST: water triple point = 273.16 K = 0.01 C = 32.018 F exactly (this was the Kelvin definition reference until 2019). Boiling point at 1 atm = 373.15 K = 100 C = 212 F

Common Mistakes

  • ✗Confusing temperature difference (delta-T) with absolute temperature - a 10 C rise equals 10 K rise (deltas are equal), but 10 C absolute is not 10 K (it's 283.15 K). Thermal resistance uses delta-T, so C/W = K/W
  • ✗Using approximate conversion 5/9 as 0.555 instead of exact 0.555556 - causes 0.008% error per conversion, accumulating in multi-stage thermal calculations
  • ✗Forgetting that Fahrenheit and Celsius scales intersect at -40 (-40 C = -40 F exactly) - this is the industrial temperature minimum per IEC 60068-2-1

Frequently Asked Questions

Absolute zero is 0 K = -273.15 C = -459.67 F exactly, where thermodynamic systems have minimum energy per the third law of thermodynamics. Per SI Brochure, Kelvin is defined via Boltzmann constant k = 1.380649 × 10^-23 J/K. Practical low temperatures: liquid nitrogen 77 K (-196 C), liquid helium 4.2 K (-269 C), superconductor operation < 100 K.
Kelvin is the SI base unit required for all thermodynamic calculations (NIST SP 811). Use Kelvin for: noise calculations (kTB), gas laws (PV = nRT), semiconductor equations (kT/q = 25.85 mV at 300 K). Use Celsius for practical engineering (junction temp, ambient). Use Fahrenheit only for US consumer applications.

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