Conversion of scales of temperature

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

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
Kelvin	x °C ≘ (x + 273.15) K	x K ≘ (x − 273.15) °C
Fahrenheit	x °C ≘ (x × ⁠9/5⁠ + 32) °F	x °F ≘ (x − 32) × ⁠5/9⁠ °C
Rankine	x °C ≘ (x + 273.15) × ⁠9/5⁠ °R	x °R ≘ (x − 491.67) × ⁠5/9⁠ °C

Kelvin scale

Temperature conversions
	from Kelvin	to Kelvin
Celsius	x K ≘ (x − 273.15) °C	x °C ≘ (x + 273.15) K
Fahrenheit	x K ≘ (x × ⁠9/5⁠ − 459.67) °F	x °F ≘ (x + 459.67) × ⁠5/9⁠ K
Rankine	x K ≘ x × ⁠9/5⁠ °R	x °R ≘ x × ⁠5/9⁠ K

Fahrenheit scale

Temperature conversions
	from Fahrenheit	to Fahrenheit
Celsius	x °F ≘ (x − 32) × ⁠5/9⁠ °C	x °C ≘ (x × ⁠9/5⁠ + 32) °F
Kelvin	x °F ≘ (x + 459.67) × ⁠5/9⁠ K	x K ≘ (x × ⁠9/5⁠ − 459.67) °F
Rankine	x °F ≘ (x + 459.67) °R	x °R ≘ (x − 459.67) °F

Rankine scale

Temperature conversions
	from Rankine	to Rankine
Celsius	x °R ≘ (x − 491.67) × ⁠5/9⁠ °C	x °C ≘ (x + 273.15) × ⁠9/5⁠ °R
Kelvin	x °R ≘ x × ⁠5/9⁠ K	x K ≘ x × ⁠9/5⁠ °R
Fahrenheit	x °R ≘ (x − 459.67) °F	x °F ≘ (x + 459.67) °R

Delisle scale

Temperature conversions
	from Delisle	to Delisle
Celsius	x °De ≘ (100 − x × ⁠2/3⁠) °C	x °C ≘ (100 − x) × ⁠3/2⁠ °De
Kelvin	x °De ≘ (373.15 − x × ⁠2/3⁠) K	x K ≘ (373.15 − x) × ⁠3/2⁠ °De
Fahrenheit	x °De ≘ (212 − x × ⁠6/5⁠) °F	x °F ≘ (212 − x) × ⁠5/6⁠ °De
Rankine	x °De ≘ (671.67 − x × ⁠6/5⁠) °R	x °R ≘ (671.67 − x) × ⁠5/6⁠ °De

Sir Isaac Newton's degree of temperature

Temperature conversions
	from Newton	to Newton
Celsius	x °N ≘ x × ⁠100/33⁠ °C	x °C ≘ x × ⁠33/100⁠ °N
Kelvin	x °N ≘ (x × ⁠100/33⁠ + 273.15) K	x K ≘ (x − 273.15) × ⁠33/100⁠ °N
Fahrenheit	x °N ≘ (x × ⁠60/11⁠ + 32) °F	x °F ≘ (x − 32) × ⁠11/60⁠ °N
Rankine	x °N ≘ (⁠60/11⁠ x + 491.67) °R	x °R ≘ (x − 491.67) × ⁠11/60⁠ °N

Réaumur scale

Temperature conversions
	from Réaumur	to Réaumur
Celsius	x °Ré ≘ x × ⁠5/4⁠ °C	x °C ≘ x × ⁠4/5⁠ °Ré
Kelvin	x °Ré ≘ (x × ⁠5/4⁠ + 273.15) K	x K ≘ (x − 273.15) × ⁠4/5⁠ °Ré
Fahrenheit	x °Ré ≘ (x × ⁠9/4⁠ + 32) °F	x °F ≘ (x − 32) × ⁠4/9⁠ °Ré
Rankine	x °Ré ≘ (x × ⁠9/4⁠ + 491.67) °R	x °R ≘ (x − 491.67) × ⁠4/9⁠ °Ré

Rømer scale

Temperature conversions
	from Rømer	to Rømer
Celsius	x °Rø ≘ (x − 7.5) × ⁠40/21⁠ °C	x °C ≘ (x × ⁠21/40⁠ + 7.5) °Rø
Kelvin	x °Rø ≘ ((x − 7.5) × ⁠40/21⁠ + 273.15) K	x K ≘ ((x − 273.15) × ⁠21/40⁠ + 7.5) °Rø
Fahrenheit	x °Rø ≘ ((x − 7.5) × ⁠24/7⁠ + 32) °F	x °F ≘ ((x − 32) × ⁠7/24⁠ + 7.5) °Rø
Rankine	x °Rø ≘ ((x − 7.5) × ⁠24/7⁠ + 491.67) °R	x °R ≘ ((x − 491.67) × ⁠7/24⁠ + 7.5) °Rø

Comparison values chart

Celsius	Fahrenheit	Kelvin	Rankine	Delisle	Newton	Réaumur	Rømer
500.00	932.00	773.15	1391.67	−600.00	165.00	400.00	270.00
490.00	914.00	763.15	1373.67	−585.00	161.70	392.00	264.75
480.00	896.00	753.15	1355.67	−570.00	158.40	384.00	259.50
470.00	878.00	743.15	1337.67	−555.00	155.10	376.00	254.25
460.00	860.00	733.15	1319.67	−540.00	151.80	368.00	249.00
450.00	842.00	723.15	1301.67	−525.00	148.50	360.00	243.75
440.00	824.00	713.15	1283.67	−510.00	145.20	352.00	238.50
430.00	806.00	703.15	1265.67	−495.00	141.90	344.00	233.25
420.00	788.00	693.15	1247.67	−480.00	138.60	336.00	228.00
410.00	770.00	683.15	1229.67	−465.00	135.30	328.00	222.75
400.00	752.00	673.15	1211.67	−450.00	132.00	320.00	217.50
390.00	734.00	663.15	1193.67	−435.00	128.70	312.00	212.25
380.00	716.00	653.15	1175.67	−420.00	125.40	304.00	207.00
370.00	698.00	643.15	1157.67	−405.00	122.10	296.00	201.75
360.00	680.00	633.15	1139.67	−390.00	118.80	288.00	196.50
350.00	662.00	623.15	1121.67	−375.00	115.50	280.00	191.25
340.00	644.00	613.15	1103.67	−360.00	112.20	272.00	186.00
330.00	626.00	603.15	1085.67	−345.00	108.90	264.00	180.75
320.00	608.00	593.15	1067.67	−330.00	105.60	256.00	175.50
310.00	590.00	583.15	1049.67	−315.00	102.30	248.00	170.25
300.00	572.00	573.15	1031.67	−300.00	99.00	240.00	165.00
290.00	554.00	563.15	1013.67	−285.00	95.70	232.00	159.75
280.00	536.00	553.15	995.67	−270.00	92.40	224.00	154.50
270.00	518.00	543.15	977.67	−255.00	89.10	216.00	149.25
260.00	500.00	533.15	959.67	−240.00	85.80	208.00	144.00
250.00	482.00	523.15	941.67	−225.00	82.50	200.00	138.75
240.00	464.00	513.15	923.67	−210.00	79.20	192.00	133.50
230.00	446.00	503.15	905.67	−195.00	75.90	184.00	128.25
220.00	428.00	493.15	887.67	−180.00	72.60	176.00	123.00
210.00	410.00	483.15	869.67	−165.00	69.30	168.00	117.75
200.00	392.00	473.15	851.67	−150.00	66.00	160.00	112.50
190.00	374.00	463.15	833.67	−135.00	62.70	152.00	107.25
180.00	356.00	453.15	815.67	−120.00	59.40	144.00	102.00
170.00	338.00	443.15	797.67	−105.00	56.10	136.00	96.75
160.00	320.00	433.15	779.67	−90.00	52.80	128.00	91.50
150.00	302.00	423.15	761.67	−75.00	49.50	120.00	86.25
140.00	284.00	413.15	743.67	−60.00	46.20	112.00	81.00
130.00	266.00	403.15	725.67	−45.00	42.90	104.00	75.75
120.00	248.00	393.15	707.67	−30.00	39.60	96.00	70.50
110.00	230.00	383.15	689.67	−15.00	36.30	88.00	65.25
100.00	212.00	373.15	671.67	0.00	33.00	80.00	60.00
90.00	194.00	363.15	653.67	15.00	29.70	72.00	54.75
80.00	176.00	353.15	635.67	30.00	26.40	64.00	49.50
70.00	158.00	343.15	617.67	45.00	23.10	56.00	44.25
60.00	140.00	333.15	599.67	60.00	19.80	48.00	39.00
50.00	122.00	323.15	581.67	75.00	16.50	40.00	33.75
40.00	104.00	313.15	563.67	90.00	13.20	32.00	28.50
30.00	86.00	303.15	545.67	105.00	9.90	24.00	23.25
20.00	68.00	293.15	527.67	120.00	6.60	16.00	18.00
10.00	50.00	283.15	509.67	135.00	3.30	8.00	12.75
0.00	32.00	273.15	491.67	150.00	0.00	0.00	7.50
−10.00	14.00	263.15	473.67	165.00	−3.30	−8.00	2.25
-14.26	6.29	258.86	465.96	171.43	-4.71	-11.43	0.00
-17.78	0.00	255.37	459.67	176.67	-5.87	-14.22	-1.83
−20.00	−4.00	253.15	455.67	180.00	−6.60	−16.00	−3.00
−30.00	−22.00	243.15	437.67	195.00	−9.90	−24.00	−8.25
−40.00	−40.00	233.15	419.67	210.00	−13.20	−32.00	−13.50
−50.00	−58.00	223.15	401.67	225.00	−16.50	−40.00	−18.75
−60.00	−76.00	213.15	383.67	240.00	−19.80	−48.00	−24.00
−70.00	−94.00	203.15	365.67	255.00	−23.10	−56.00	−29.25
−80.00	−112.00	193.15	347.67	270.00	−26.40	−64.00	−34.50
−90.00	−130.00	183.15	329.67	285.00	−29.70	−72.00	−39.75
−100.00	−148.00	173.15	311.67	300.00	−33.00	−80.00	−45.00
−110.00	−166.00	163.15	293.67	315.00	−36.30	−88.00	−50.25
−120.00	−184.00	153.15	275.67	330.00	−39.60	−96.00	−55.50
−130.00	−202.00	143.15	257.67	345.00	−42.90	−104.00	−60.75
−140.00	−220.00	133.15	239.67	360.00	−46.20	−112.00	−66.00
−150.00	−238.00	123.15	221.67	375.00	−49.50	−120.00	−71.25
−160.00	−256.00	113.15	203.67	390.00	−52.80	−128.00	−76.50
−170.00	−274.00	103.15	185.67	405.00	−56.10	−136.00	−81.75
−180.00	−292.00	93.15	167.67	420.00	−59.40	−144.00	−87.00
−190.00	−310.00	83.15	149.67	435.00	−62.70	−152.00	−92.25
−200.00	−328.00	73.15	131.67	450.00	−66.00	−160.00	−97.50
−210.00	−346.00	63.15	113.67	465.00	−69.30	−168.00	−102.75
−220.00	−364.00	53.15	95.67	480.00	−72.60	−176.00	−108.00
−230.00	−382.00	43.15	77.67	495.00	−75.90	−184.00	−113.25
−240.00	−400.00	33.15	59.67	510.00	−79.20	−192.00	−118.50
−250.00	−418.00	23.15	41.67	525.00	−82.50	−200.00	−123.75
−260.00	−436.00	13.15	23.67	540.00	−85.80	−208.00	−129.00
−270.00	−454.00	3.15	5.67	555.00	−89.10	−216.00	−134.25
−273.15	−459.67	0.00	0.00	559.725	−90.1395	−218.52	−135.90375
Celsius	Fahrenheit	Kelvin	Rankine	Delisle	Newton	Réaumur	Rømer

Comparison of temperature scales

**Comparison of temperature scales**
Comment	Kelvin	Celsius	Fahrenheit	Rankine	Delisle	Newton	Réaumur	Rømer
Absolute zero	0.00	−273.15	−459.67	0.00	559.73	−90.14	−218.52	−135.90
Lowest recorded surface temperature on Earth^[1]	184	−89.2^[1]	−128.6^[1]	331	284	−29	−71	−39
Fahrenheit's ice/salt mixture	255.37	−17.78	0.00	459.67	176.67	−5.87	−14.22	−1.83
Ice melts (at standard pressure)	273.15	0.00	32.00	491.67	150.00	0.00	0.00	7.50
Triple point of water	273.16	0.01	32.018	491.688	149.985	0.0033	0.008	7.50525
Average surface temperature on Earth	288	15	59	519	128	5	12	15
Average human body temperature*	310	37	98	558	95	12	29	27
Highest recorded surface temperature on Earth^[2]	331	58^[2]	136.4^[2]	596	63	19	46	38
Water boils (at standard pressure)	373.1339	99.9839	211.97102^[3]	671.64102^[3]	0.00	33.00	80.00	60.00
Titanium melts	1941	1668	3034	3494	−2352	550	1334	883
The surface of the Sun	5800	5500	9900	10400	−8100	1800	4400	2900

* 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.^[4]

Some numbers in this table have been rounded.

Graphical representation

								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

Notes and references

^ ^a ^b ^c ^d 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).
^ ^a ^b ^c ^d "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."
^ ^a ^b "Comparison of temperature scales". Tampile.
^ Wong, Lena (1997). Elert, Glenn (ed.). "Temperature of a healthy human (body temperature)". The Physics Factbook. Retrieved 2018-06-07.

[VS-1] 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).

[ASU-2] "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."

[TAM-3] "Comparison of temperature scales". Tampile.

[4] Wong, Lena (1997). Elert, Glenn (ed.). "Temperature of a healthy human (body temperature)". The Physics Factbook. Retrieved 2018-06-07.

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