One mmHg is the pressure exerted by a 1 mm vertical column of mercury (Hg) at 0 degree Celsius. One mmHg is virtually equal to 1 torr, which is defined as 1/760 of 1 atmosphere (atm) pressure (i.e., 1 atm = 760 mmHg). The unit of mmHg is considered obsolete, and the SI unit “Pascal” (Pa; 1 atm = 101,325 Pa ) should be used. Nevertheless, mmHg is still widely used in medicine to express blood pressure. The steps below demonstrate several examples of calculating mmHg.

Calculate the blood pressure of 120 mmHg using the basic definition of mmHg:

Pressure = Hg density * Standard gravity * Mercury height

Hg density is 13.5951 g/cm^3 (13595.1 kg/m^3), and standard gravity is 9.80665 m/s^2. Note that 120 mm is 0.12 m.

Pressure = 13595.1 kg/m^3 * 9.80665 m/s^2 * 0.12 m = 15998.69 Pa

Obtain the relation between 1 Pa and 1 mmHg. Consider that 1 atm = 101,325 Pa, and 1 atm = 760 mmHg. Hence 101,325 Pa = 760 mmHg. Multiplying both sides of the equation by 1/760 you would get:

1 mmHg = 1 Pa * 101,325 / 760

Find the formula to convert pressure in Pa to mmHg using the proportion:

1 mmHg corresponds to 1 Pa * 101,325/760 Pressure (mmHg) corresponds to Pressure (Pa)

The solution of this proportion produces the formula:

Pressure (mmHg) = Pressure (Pa) * 760 / 101,325 = Pressure (Pa) * 0.0075

Calculate the pressure of 35,000 Pa in mmHg using the formula from Step 3:

Pressure = 35,000 Pa * 0.0075 = 262.5 mmHg

#### References

- Quantities, Units and Symbols in Physical Chemistry; E.R. Cohen, T. Cvitas, J.G. Frey and B. Holstrom; 2007