# Torr

(Redirected from MmHg)

Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]

The torr (symbol: Torr) is a non-SI unit of pressure defined as 1/760 of an atmosphere. It was named after Evangelista Torricelli, an Italian physicist and mathematician who discovered the principle of the barometer in 1644.[1]

## History

Torricelli attracted considerable attention when he demonstrated the first mercury barometer to the general public. He is credited with giving the first modern explanation of atmospheric pressure. Scientists at the time were familiar with small fluctuations in height that occurred in barometers. When these fluctuations were explained as a manifestation of changes in atmospheric pressure, the science of meteorology was born.

Over time, 760 millimeters of mercury came to be regarded as the “standard” atmospheric pressure. The unit of barometric pressure (one millimeter of mercury, also written as 1 mm Hg) was named in honor of Torricelli.

In 1954, the definition of atmosphere was revised by the 10e Conférence Générale des Poids et Mesures (10th CGPM)[2] to the currently accepted definition: one atmosphere is equal to 101325 pascals. The torr was then re-defined as 1/760 of one atmosphere. This change in the definition of “torr” has been a source of confusion ever since.

## SI units of pressure

The SI unit of pressure is the pascal (symbol: Pa), defined as one newton per square meter. Other units of pressure are defined in terms of SI units.[3][4] These include:

• The bar (symbol: bar), defined as 105 Pa exactly.
• The atmosphere (symbol: atm), defined as 101,325 Pa exactly.
• The torr (symbol: Torr), defined as 1/760 atm exactly.

These four SI-related pressure units are used in different settings. For example, the bar is used in meteorology to report atmospheric pressures.[5] The torr, a more convenient unit for low pressures, is used in high-vacuum physics and engineering.

Pressure Units

pascal
(Pa)

bar
(bar)
technical atmosphere
(at)

atmosphere
(atm)

torr
(Torr)
pound-force per
square inch

(psi)
1 Pa ≡ 1 N/m2 10−5 1.0197×10−5 9.8692×10−6 7.5006×10−3 145.04×10−6
1 bar 100,000 ≡ 106 dyn/cm2 1.0197 0.98692 750.06 14.504
1 at 98,066.5 0.980665 ≡ 1 kgf/cm2 0.96784 735.56 14.223
1 atm 101,325 1.01325 1.0332 ≡ 1 atm 760 14.696
1 torr 133.322 1.3332×10−3 1.3595×10−3 1.3158×10−3 ≡ 1 Torr; ≈ 1 mmHg 19.337×10−3
1 psi 6,894.76 68.948×10−3 70.307×10−3 68.046×10−3 51.715 ≡ 1 lbf/in2

Example reading:  1 Pa = 1 N/m2  = 10−5 bar  = 10.197×10−6 at  = 9.8692×10−6 atm, etc.
Note:  mmHg is an abbreviation for millimetres of mercury.

## Manometric units of pressure

Manometric units are units such as millimeters of mercury or centimeters of water that depend on an assumed density of a fluid and an assumed acceleration of gravity. These units are now regarded as obsolete, and their use is discouraged.[6] Nevertheless, manometric units are used routinely in medicine and physiology, and they continue to be used in areas as diverse as weather reporting and scuba diving.

The millimeter of mercury (symbol: mmHg) is defined as the pressure exerted at the base of a column of fluid exactly 1 mm high, when the density of the fluid is exactly 13.5951 g/cm³, at a place where the acceleration of gravity is exactly 9.80665 m/s².[7]

• A fluid density of 13.5951 g/cm³ was chosen for this definition because this is the approximate density of mercury at 0 °C. The definition, therefore, assumes a particular value for the density of mercury. This assumption limits the precision of any pressure measurement (in mmHg) to six significant digits.[8]
• The definition assumes a particular value for the acceleration of gravity: the standard acceleration gn = 9.80665 m/sec2. In practice, of course, measurements are made using local values.

These assumptions limit both the validity and the precision of the mmHg as a unit of pressure. No metrology laboratory measures or calibrates pressure directly in these terms. It would be extremely difficult to find a fluid with exactly this density, and a place where g was exactly 9.80665 m/s². According to the UK’s National Physical Laboratory (NPL):

The need to assume fixed and exact but ultimately incorrect values of
liquid density and acceleration due to gravity inherently limits knowledge
of the relationship between [the millimeter of mercury] and the pascal.
By contrast, the magnitude of pressure values expressed in the SI pressure
unit, the pascal, can flex (albeit not by much) to take account of technological
improvements in the underlying definitions of mass, length and time – the
SI base quantities from which pressure is derived.[9]

The performance of modern transducers approaches the precision required to distinguish between the torr and the millimeter of mercury. The NPL concludes

Thus, in the near future, the accuracy claims being made for otherwise
state-of-the-art instruments scaled in manometric units will become
inherently inferior. Even now, confusion and large errors abound through
the use of differing definitions, including alternative values of ‘standard’
gravity and varying assumptions about the density and temperature of the
to errors of several tenths of a percent and there are many stories of this
leading to major mistakes in pressure measurement.

### Manometric units in medicine and physiology

In medicine, the mmHg (measured with a sphygmomanometer) is the gold standard for blood pressure measurement. In physiology, manometric units are used to measure Starling forces. Other applications include:

Manometric results in medicine are sometimes given in torr. This is usually incorrect, since the Torr and the mmHg are not the same thing. Pressures obtained with a manometer (or its transducer equivalent) should be reported in mmHg.

## Conversion factors

The mmHg is defined as 13.5951 x 9.80665 = 133.322387415 Pa. This is an exact number, although it is too long to be of any practical use.

The torr is defined as 1/760 of one atmosphere, while the atmosphere is defined as 101,325 Pa. Therefore, one Torr is equal to 101325/760 of one Pa. The decimal form of this fraction (133.322368421...) is, unfortunately, an infinitely long, periodically repeating decimal.

The relationship between the Torr and the mmHg is:

```                                Torr = 0.999 999 857 533 699... mmHg
1 mmHg = 1.000 000 142 466 321... Torr
```

The mmHg and the Torr differ from one another by less than 2 x 10-7 Torr. The difference between one atmosphere (101325 Pa) and 760 mmHg (101325.0144354 Pa) less than 0.2 μPa/Pa (less than 0.00002%). This small difference is negligible for most applications outside metrology.

## Notes

1. Devices similar to the modern barometer, using water instead of mercury, were studied by a number of scientists in the early 1640s (http://www.strange-loops.com/scibarometer.html). Torricelli’s explanation of the principle of the barometer appears in a letter to Michelangelo Ricci (http://web.lemoyne.edu/~guinta/torr.html) dated June 11, 1644.
2. http://www.bipm.org/en/CGPM/db/10/4/
3. Cohen ER et. al. Quantities, Units and Symbols in Physical Chemistry, 3rd ed. Royal Society of Chemistry, 2007.
4. DeVoe H. Thermodynamics and Chemistry. Prentice-Hall, Inc. 2001.
5. Note that a pressure of 1 bar (100,000 Pa) is slightly less than a pressure of 1 atmosphere (101,325 Pa).
6. National Physical Laboratory: Pressure units. http://www.npl.co.uk/pressure/punits.htm.
7. Conventional millimeters of mercury. http://www.sizes.com/units/mmHg.htms.
8. The density of mercury is now known to 6 decimal places (8 significant digits). See, for example, http://www.cstl.nist.gov/div836/836.05/papers/Strouse01TM_HG_TP_cells.pdf.
9. National Physical Laboratory: Pressure and vacuum. http://www.npl.co.uk/pressure/faqs/unitvalidity.html