Understanding Centimeters of Mercury to Standard Atmospheres Conversion
A centimeter of mercury (cmHg) measures pressure by mercury-column height, and the standard atmosphere (atm) is a fixed reference pressure defined as 101325 pascals, roughly the mean sea-level air pressure. Since a standard atmosphere corresponds to a 76 cm mercury column, each centimeter of mercury is a small fraction of an atmosphere. This conversion is widely used in chemistry, physics, and gas-law calculations where atmospheres are the natural unit.
Conversion Formula
To convert centimeters of mercury to standard atmospheres, multiply by this factor:
Step-by-Step Example
Convert 25 centimeters of mercury to standard atmospheres.
How to Convert Centimeters of Mercury to Standard Atmospheres
Express a mercury-column pressure as a fraction of the standard sea-level atmosphere for gas-law work.
- Take the cmHg reading: Begin with the pressure in centimeters of mercury.
- Multiply by 0.0131579: This factor converts centimeters of mercury into standard atmospheres.
- State the result: For example, 25 cmHg × 0.0131579 = 0.328948 atm.
- Check the reverse: Multiply the atm value by 76 to return to cmHg.
centimeters of mercury to standard atmospheres conversion table
| centimeters of mercury (cmHg) | standard atmospheres (atm) |
|---|---|
| 0 | 0 |
| 1 | 0.0131579 |
| 2 | 0.02631579 |
| 3 | 0.03947369 |
| 4 | 0.05263159 |
| 5 | 0.06578948 |
| 6 | 0.07894738 |
| 7 | 0.09210528 |
| 8 | 0.1052632 |
| 9 | 0.1184211 |
| 10 | 0.131579 |
| 15 | 0.1973684 |
| 20 | 0.2631579 |
| 25 | 0.3289474 |
| 30 | 0.3947369 |
| 40 | 0.5263159 |
| 50 | 0.6578948 |
| 60 | 0.7894738 |
| 70 | 0.9210528 |
| 80 | 1.052632 |
| 90 | 1.184211 |
| 100 | 1.31579 |
| 150 | 1.973684 |
| 200 | 2.631579 |
| 250 | 3.289474 |
| 300 | 3.947369 |
| 400 | 5.263159 |
| 500 | 6.578948 |
| 600 | 7.894738 |
| 700 | 9.210528 |
| 800 | 10.52632 |
| 900 | 11.84211 |
| 1000 | 13.1579 |
| 2000 | 26.31579 |
| 3000 | 39.47369 |
| 4000 | 52.63159 |
| 5000 | 65.78948 |
| 10000 | 131.579 |
| 25000 | 328.9474 |
| 50000 | 657.8948 |
| 100000 | 1315.79 |
| 250000 | 3289.474 |
| 500000 | 6578.948 |
| 1000000 | 13157.9 |
What is the centimeter of mercury?
The centimeter of mercury (cmHg) is a unit of pressure equal to the pressure exerted by a one-centimeter-high column of mercury under standard conditions. It is a scaled-up form of the millimeter of mercury (torr) used in some scientific and industrial settings.
Definition
The conventional centimeter of mercury is based on a 1 cm column of mercury with a density of 13,595.1 kg/m³ under standard gravity (9.80665 m/s²):
Exactly, 1 cmHg = 1333.22387415 Pa, which is ten times the millimeter of mercury (1 mmHg ≈ 133.322 Pa). This equals 10 torr under the conventional definition.
Origin and History
The unit descends directly from Torricelli's mercury barometer of 1643, where atmospheric pressure was read as the height of a mercury column. Mercury's high density makes the column compact and easy to read. The conventional value fixes mercury's density (its value at 0 °C) and standard gravity so the unit is independent of temperature and location.
Law and Notable Facts
The centimeter of mercury is not an SI unit; the SI unit of pressure is the pascal. It relates to the standard atmosphere as 1 atm = 76 cmHg exactly (by the historical 760 mmHg definition). The millimeter of mercury (mmHg), essentially identical to the torr, remains standard in medicine for blood pressure.
Real-World Examples and Conversions
- 1 cmHg = 10 mmHg (10 torr) ≈ 1.33322 kPa.
- One standard atmosphere equals exactly 76 cmHg.
- A blood pressure of 120/80 mmHg corresponds to 12/8 cmHg.
- A vacuum of 5 cmHg absolute is about 6.7 kPa, roughly 93% below atmospheric pressure.
What is the standard atmosphere?
The standard atmosphere (atm) is a unit of pressure defined as a fixed reference value close to the average atmospheric pressure at sea level. It is widely used in chemistry, physics, engineering, and diving to express pressures relative to typical sea-level conditions.
Definition
The standard atmosphere is defined exactly as 101,325 pascals:
This is equivalent to 1013.25 hectopascals (millibars), 760 millimeters of mercury (torr), and about 14.6959 pounds per square inch. The value was fixed by the 10th General Conference on Weights and Measures (CGPM) in 1954.
Origin and History
Early pressure measurement grew from Evangelista Torricelli's 1643 barometer experiments, which showed the atmosphere supports a mercury column about 760 mm high. The "atmosphere" became a convenient reference for a whole unit of ambient pressure. In 1954 the CGPM adopted the exact value 101,325 Pa, based on a 760 mm mercury column at 0 °C under standard gravity, to remove the temperature and location dependence of earlier definitions.
Law and Notable Facts
The standard atmosphere is accepted for use with the SI but is not an SI unit; the SI unit of pressure is the pascal. IUPAC now recommends the bar (100,000 Pa) rather than the atmosphere as the standard pressure for reporting thermodynamic data, though "atm" remains common. Note that the technical atmosphere (at) is a different unit equal to 98,066.5 Pa.
Real-World Examples and Conversions
- Average sea-level air pressure is very close to 1 atm (101.325 kPa).
- Ocean pressure increases by roughly 1 atm for every 10 meters of seawater depth, so a diver at 30 m experiences about 4 atm total.
- A typical car tire inflated to 32 psi holds about 2.2 atm of gauge pressure.
- The pressure inside a champagne bottle is roughly 6 atm (about 608 kPa).
Frequently Asked Questions
How many atmospheres are in one centimeter of mercury?
One centimeter of mercury equals 0.0131579 standard atmospheres, since a full atmosphere is a 76 cmHg column.
How many centimeters of mercury make one atmosphere?
Exactly 76 cmHg, because multiplying 76 by 0.0131579 returns 1 atm.
How do I convert atmospheres back to centimeters of mercury?
Multiply the atmosphere value by 75.99999 (essentially 76), the reciprocal of 0.0131579.
Why is the atmosphere useful in chemistry?
Gas laws such as the ideal gas equation are often tabulated with pressures in atmospheres, so converting cmHg to atm simplifies those calculations.
What is 38 cmHg in atmospheres?
38 cmHg equals about 0.5 atm (38 × 0.0131579), or half a standard atmosphere.
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Complete centimeters of mercury conversion table
| Unit | Result |
|---|---|
| pascals (Pa) | 1333.224 Pa |
| kilopascals (kPa) | 1.333224 kPa |
| megapascals (MPa) | 0.001333224 MPa |
| hectopascals (hPa) | 13.33224 hPa |
| millibar (mbar) | 13.33224 mbar |
| bar (bar) | 0.01333224 bar |
| torr (torr) | 10 torr |
| meters of water @ 4°C (mH2O) | 0.135951 mH2O |
| millimeters of mercury (mmHg) | 10 mmHg |
| standard atmospheres (atm) | 0.0131579 atm |
| centimeters of water (cmH2O) | 13.5951 cmH2O |
| technical atmospheres (at) | 0.0135951 at |
| pounds per square inch (psi) | 0.1933678 psi |
| kilopound per square inch (ksi) | 0.0001933678 ksi |
| Inches of mercury (inHg) | 0.3937008 inHg |