Conversion of scales of temperature

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This is a collection of temperature conversion formulas and comparisons among eight different temperature scales, several of which have long been obsolete.

Contents

Temperatures on scales that either do not share a numeric zero or are nonlinearly related cannot correctly be mathematically equated (related using the symbol =), and thus temperatures on different scales are more correctly described as corresponding (related using the symbol ≘).

Celsius scale

Temperature conversions
from Celsius to Celsius
Kelvinx °C  (x + 273.15) Kx K  (x  273.15) °C
Fahrenheitx °C  (x × 9/5 + 32) °Fx °F  (x  32) × 5/9 °C
Rankinex °C  (x + 273.15) × 9/5 °Rx °R  (x  491.67) × 5/9 °C

Kelvin scale

Temperature conversions
from Kelvin to Kelvin
Celsiusx K  (x  273.15) °Cx °C  (x + 273.15) K
Fahrenheitx K  (x × 9/5  459.67) °Fx °F  (x + 459.67) × 5/9 K
Rankinex K  x × 9/5 °Rx °R  x × 5/9 K

Fahrenheit scale

Temperature conversions
from Fahrenheit to Fahrenheit
Celsiusx °F  (x  32) × 5/9 °Cx °C  (x × 9/5 + 32) °F
Kelvinx °F  (x + 459.67) × 5/9 Kx K  (x × 9/5  459.67) °F
Rankinex °F  (x + 459.67) °Rx °R  (x  459.67) °F

Rankine scale

Temperature conversions
from Rankine to Rankine
Celsiusx °R  (x  491.67) × 5/9 °Cx °C  (x + 273.15) × 9/5 °R
Kelvinx °R  x × 5/9 Kx K  x × 9/5 °R
Fahrenheitx °R  (x  459.67) °Fx °F  (x + 459.67) °R

Delisle scale

Temperature conversions
from Delisle to Delisle
Celsiusx °De  (100  x × 2/3) °Cx °C  (100  x) × 3/2 °De
Kelvinx °De  (373.15  x × 2/3) Kx K  (373.15  x) × 3/2 °De
Fahrenheitx °De  (212  x × 6/5) °Fx °F  (212  x) × 5/6 °De
Rankinex °De  (671.67  x × 6/5) °Rx °R  (671.67  x) × 5/6 °De

Newton scale

Temperature conversions
from Newton to Newton
Celsiusx °N  x × 100/33 °Cx °C  x × 33/100 °N
Kelvinx °N  (x × 100/33 + 273.15) Kx K  (x  273.15) × 33/100 °N
Fahrenheitx °N  (x × 60/11 + 32) °Fx °F  (x  32) × 11/60 °N
Rankinex °N  (60/11 x + 491.67) °Rx °R  (x  491.67) × 11/60 °N

Réaumur scale

Temperature conversions
from Réaumur to Réaumur
Celsiusx °Ré  x × 5/4 °Cx °C  x × 4/5 °Ré
Kelvinx °Ré  (x × 5/4 + 273.15) Kx K  (x  273.15) × 4/5 °Ré
Fahrenheitx °Ré  (x × 9/4 + 32) °Fx °F  (x  32) × 4/9 °Ré
Rankinex °Ré  (x × 9/4 + 491.67) °Rx °R  (x  491.67) × 4/9 °Ré

Rømer scale

Temperature conversions
from Rømer to Rømer
Celsiusx °Rø  (x  7.5) × 40/21 °Cx °C  (x × 21/40 + 7.5) °Rø
Kelvinx °Rø  ((x  7.5) × 40/21 + 273.15) Kx K  ((x  273.15) × 21/40 + 7.5) °Rø
Fahrenheitx °Rø  ((x  7.5) × 24/7 + 32) °Fx °F  ((x  32) × 7/24 + 7.5) °Rø
Rankinex °Rø  ((x  7.5) × 24/7 + 491.67) °Rx °R  ((x  491.67) × 7/24 + 7.5) °Rø

Comparison values chart

CelsiusFahrenheitKelvinRankineDelisleNewtonRéaumurRømer
500.00932.00773.151391.67−600.00165.00400.00270.00
490.00914.00763.151373.67−585.00161.70392.00264.75
480.00896.00753.151355.67−570.00158.40384.00259.50
470.00878.00743.151337.67−555.00155.10376.00254.25
460.00860.00733.151319.67−540.00151.80368.00249.00
450.00842.00723.151301.67−525.00148.50360.00243.75
440.00824.00713.151283.67−510.00145.20352.00238.50
430.00806.00703.151265.67−495.00141.90344.00233.25
420.00788.00693.151247.67−480.00138.60336.00228.00
410.00770.00683.151229.67−465.00135.30328.00222.75
400.00752.00673.151211.67−450.00132.00320.00217.50
390.00734.00663.151193.67−435.00128.70312.00212.25
380.00716.00653.151175.67−420.00125.40304.00207.00
370.00698.00643.151157.67−405.00122.10296.00201.75
360.00680.00633.151139.67−390.00118.80288.00196.50
350.00662.00623.151121.67−375.00115.50280.00191.25
340.00644.00613.151103.67−360.00112.20272.00186.00
330.00626.00603.151085.67−345.00108.90264.00180.75
320.00608.00593.151067.67−330.00105.60256.00175.50
310.00590.00583.151049.67−315.00102.30248.00170.25
300.00572.00573.151031.67−300.0099.00240.00165.00
290.00554.00563.151013.67−285.0095.70232.00159.75
280.00536.00553.15995.67−270.0092.40224.00154.50
270.00518.00543.15977.67−255.0089.10216.00149.25
260.00500.00533.15959.67−240.0085.80208.00144.00
250.00482.00523.15941.67−225.0082.50200.00138.75
240.00464.00513.15923.67−210.0079.20192.00133.50
230.00446.00503.15905.67−195.0075.90184.00128.25
220.00428.00493.15887.67−180.0072.60176.00123.00
210.00410.00483.15869.67−165.0069.30168.00117.75
200.00392.00473.15851.67−150.0066.00160.00112.50
190.00374.00463.15833.67−135.0062.70152.00107.25
180.00356.00453.15815.67−120.0059.40144.00102.00
170.00338.00443.15797.67−105.0056.10136.0096.75
160.00320.00433.15779.67−90.0052.80128.0091.50
150.00302.00423.15761.67−75.0049.50120.0086.25
140.00284.00413.15743.67−60.0046.20112.0081.00
130.00266.00403.15725.67−45.0042.90104.0075.75
120.00248.00393.15707.67−30.0039.6096.0070.50
110.00230.00383.15689.67−15.0036.3088.0065.25
100.00212.00373.15671.670.0033.0080.0060.00
90.00194.00363.15653.6715.0029.7072.0054.75
80.00176.00353.15635.6730.0026.4064.0049.50
70.00158.00343.15617.6745.0023.1056.0044.25
60.00140.00333.15599.6760.0019.8048.0039.00
50.00122.00323.15581.6775.0016.5040.0033.75
40.00104.00313.15563.6790.0013.2032.0028.50
30.0086.00303.15545.67105.009.9024.0023.25
20.0068.00293.15527.67120.006.6016.0018.00
10.0050.00283.15509.67135.003.308.0012.75
0.0032.00273.15491.67150.000.000.007.50
−10.0014.00263.15473.67165.00−3.30−8.002.25
-14.266.29258.86465.96171.43-4.71-11.430.00
-17.780.00255.37459.67176.67-5.87-14.22-1.83
−20.00−4.00253.15455.67180.00−6.60−16.00−3.00
−30.00−22.00243.15437.67195.00−9.90−24.00−8.25
−40.00−40.00233.15419.67210.00−13.20−32.00−13.50
−50.00−58.00223.15401.67225.00−16.50−40.00−18.75
−60.00−76.00213.15383.67240.00−19.80−48.00−24.00
−70.00−94.00203.15365.67255.00−23.10−56.00−29.25
−80.00−112.00193.15347.67270.00−26.40−64.00−34.50
−90.00−130.00183.15329.67285.00−29.70−72.00−39.75
−100.00−148.00173.15311.67300.00−33.00−80.00−45.00
−110.00−166.00163.15293.67315.00−36.30−88.00−50.25
−120.00−184.00153.15275.67330.00−39.60−96.00−55.50
−130.00−202.00143.15257.67345.00−42.90−104.00−60.75
−140.00−220.00133.15239.67360.00−46.20−112.00−66.00
−150.00−238.00123.15221.67375.00−49.50−120.00−71.25
−160.00−256.00113.15203.67390.00−52.80−128.00−76.50
−170.00−274.00103.15185.67405.00−56.10−136.00−81.75
−180.00−292.0093.15167.67420.00−59.40−144.00−87.00
−190.00−310.0083.15149.67435.00−62.70−152.00−92.25
−200.00−328.0073.15131.67450.00−66.00−160.00−97.50
−210.00−346.0063.15113.67465.00−69.30−168.00−102.75
−220.00−364.0053.1595.67480.00−72.60−176.00−108.00
−230.00−382.0043.1577.67495.00−75.90−184.00−113.25
−240.00−400.0033.1559.67510.00−79.20−192.00−118.50
−250.00−418.0023.1541.67525.00−82.50−200.00−123.75
−260.00−436.0013.1523.67540.00−85.80−208.00−129.00
−270.00−454.003.155.67555.00−89.10−216.00−134.25
−273.15−459.670.000.00559.725−90.1395−218.52−135.90375
CelsiusFahrenheitKelvinRankineDelisleNewtonRéaumurRømer

Comparison of temperature scales

Comparison of temperature scales
Comment Kelvin Celsius Fahrenheit Rankine Delisle Newton Réaumur Rømer
Absolute zero 0.00−273.15−459.670.00559.73−90.14−218.52−135.90
Lowest recorded surface temperature on Earth [1] 184−89.2 [1] −128.6 [1] 331284−29−71−39
Fahrenheit's ice/salt mixture255.37−17.780.00459.67176.67−5.87−14.22−1.83
Ice melts (at standard pressure)273.150.0032.00491.67150.000.000.007.50
Triple point of water273.160.0132.018491.688149.9850.00330.0087.50525
Average surface temperature on Earth288155951912851215
Average human body temperature*310379855895122927
Highest recorded surface temperature on Earth [2] 33158 [2] 136.4 [2] 59663194638
Water boils (at standard pressure)373.133999.9839211.97102671.641020.0033.0080.0060.00
Titanium melts1941166830343494−23525501334883
The surface of the Sun 58005500990010400−8100180044002900

* Normal human body temperature is 36.8 °C ±0.7 °C, or 98.2 °F ±1.3 °F. The commonly given value 98.6 °F is simply the exact conversion of the nineteenth-century German standard of 37 °C. Since it does not list an acceptable range, it could therefore be said to have excess (invalid) precision. [3]

Some numbers in this table have been rounded.

Graphical representation

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Rankine (°R)
Kelvin (K)
Fahrenheit (°F)
Celsius (°C)
Réaumur (°Ré)
Rømer (°Rø)
Newton (°N)
Delisle (°D)
Absolute zero Lowest recorded surface temperature on Earth [1] Fahrenheit's ice/water/salt mixture Melting point of ice (at standard pressure)Average surface temperature on Earth (15 °C)Average human body temperature (37 °C) Highest recorded surface temperature on Earth [2] Boiling point of water (at standard pressure) 

Conversion table between the different temperature units

KelvinConversion of scales of temperature


CelsiusConversion of scales of temperature


FahrenheitConversion of scales of temperature


Rankine scaleConversion of scales of temperature


Rømer scaleConversion of scales of temperature


Newton scaleConversion of scales of temperature


Delisle scaleConversion of scales of temperature


Réaumur scaleConversion of scales of temperature

Converting units of temperature differences

Converting units of temperature differences (also referred to as temperature deltas) is not the same as converting absolute temperature values, and different formulae must be used.

To convert a delta temperature from Fahrenheit to Celsius, the formula is T}°F = 9/5T}°C.

To convert a delta temperature from Celsius to Kelvin, it is 1:1 ({ΔT}°C = {ΔT}K).

See also

Notes and references

  1. 1 2 3 4 The Coldest Inhabited Places on Earth; researchers of the Vostok Station recorded the coldest known temperature on Earth on July 21st 1983: −89.2 °C (−128.6 °F).
  2. 1 2 3 4 "World: Highest Temperature". Arizona State University, School of Geographical Sciences. November 12, 2007. Archived from the original on January 4, 2013. an Italian weather station in al 'Aziziyah (Libya) measured a temperature of 58 °C (136.4 °F) on September 13th 1922. "Although this record has gained general acceptance as the world's highest temperature recorded under standard conditions, the validity of the extreme has been questioned."
  3. Wong, Lena (1997). Elert, Glenn (ed.). "Temperature of a healthy human (body temperature)". The Physics Factbook. Retrieved 2018-06-07.

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