# Convert Pressure Units

- 1

Current unit

## Pressure Dimensional Analysis

The dimensional analysis stems from the interrelation of two other quantities: force and area.

```
Pressure = force / area
= M¹ L¹ / T² / L²
= M¹ L⁻¹ T⁻²
```

## Pressure Conversion Factors

Pressure can be expressed in various units depending on the system of measurement used. In the International System (SI) or metric system, pressure is measured in units of Pascal (Pa), kilopascal (kPa), or megapascal (MPa). In the US system (US/British Customary units), you'll often encounter pounds-force per square foot (psf) or pounds-force per square inch (psi).

To convert between these units, we use conversion factors. The tables below provide some commonly used conversion factors for pressure units.

**Conversion factors rounded to three significant figures**:

Ref | Pa | kPa | MPa |
---|---|---|---|

1 Pa | 1 | 0.001 | 0.000001 |

1 kPa | 1000 | 1 | 0.001 |

1 MPa | 1000000 | 1000 | 1 |

1 psf | 47.9 | 0.0479 | 4.79e-5 |

1 psi | 6890 | 6.89 | 0.00689 |

Ref | psf | psi |
---|---|---|

1 Pa | 0.0209 | 1.45e-4 |

1 kPa | 20.9 | 0.145 |

1 MPa | 20900 | 145 |

1 psf | 1 | 0.00694 |

1 psi | 144 | 1 |

**Conversion factors in scientific notation with eight decimal places** for greater precision:

Ref | Pa | kPa | MPa |
---|---|---|---|

1 Pa | 1.00000000e+0 | 1.00000000e-3 | 1.00000000e-6 |

1 kPa | 1.00000000e+3 | 1.00000000e+0 | 1.00000000e-3 |

1 MPa | 1.00000000e+6 | 1.00000000e+3 | 1.00000000e+0 |

1 psf | 4.78802590e+1 | 4.78802590e-2 | 4.78802590e-5 |

1 psi | 6.89475729e+3 | 6.89475729e+0 | 6.89475729e-3 |

Ref | psf | psi |
---|---|---|

1 Pa | 2.08854342e-2 | 1.45037738e-4 |

1 kPa | 2.08854342e+1 | 1.45037738e-1 |

1 MPa | 2.08854342e+4 | 1.45037738e+2 |

1 psf | 1.00000000e+0 | 6.94444444e-2 |

1 psi | 1.44000000e+2 | 1.00000000e+0 |

## How to Use the Pressure Conversion Factors

Using the conversion factors shown in the previous tables, you can easily convert units manually. Let's say you have a pressure of 2500 psf (US units), and want to convert it to the metric unit of kPa. If you just need a quick estimate, you can use the factors from the first tables. But, which one?

We have two options:

- If we read it as
`1 kPa`

equals`20.9 psf`

, you can go to the first column, find the row`1 kPa`

, and check the cell at the`psf`

column:

```
2500 psf · (1 kPa) / (20.9 psf)
= 2500 / 20.9 kPa
= 120 kPa
```

- If we read it as
`1 psf`

equals`0.0479 kPa`

, you can go to the first column, find the row`1 psf`

, and check the cell at the`kPa`

column:

```
2500 psf · (0.0479 kPa) / (1 psf)
= 2500 · 0.0479 kN/m³
= 20.4 kN/m³
```

Similarly, you can apply the same process to use the more accurate conversion factors provided in the later tables.

## Understanding Pressure, Stress, and Strength

Pressure, stress, and strength are interconnected yet distinct concepts. Pressure is the force spread over an area, often seen when fluids or weights push on surfaces. Stress, however, goes inside materials, and describes the internal forces in an object during deformation, which can be due to external pressures. Strength measures how much stress materials can handle before breaking. So, pressure is about external push on an object, stress is internal forces of the object, and strength is about how much stress can the object material resist.

Both pressure, stress, and strength are measured using the same units. We can say that all three belong to the physical quantity of pressure.

To demystify these concepts, let's delve into a simplified and intuitive example.

Imagine you're going to pierce your ear to wear earrings. Your first option will probably be to do it with a needle, which may have a slender tip diameter of 1 mm. This slender needle makes piercing your skin relatively effortless.

Now imagine that instead of the needle you use the back of a marker, which has a diameter of 20 mm. Would piercing your sking be as simple? It doesn't seem so. It may even be hard to believe that you can pierce your skin with the marker at all. But in any case, you'll need much more force to do it.

How much more force would you need? Let's see.

You can assume that the applied pressure produces an equivalent internal stress in the skin.

```
pressure = force / area
stress = pressure
stress = force / area
```

You'll need the stress in the skin to reach the strength limit in order to pierce it.

```
stress = strength
stress = force / area
strength = force / area
```

You can now isolate the force needed to reach the strength limit, and so pierce your skin:

```
force = strength · area
```

Given that the skin is exactly the same, its strength limit will also be the same in both cases. You can then compare the spread area of both objects:

```
Needle area = π / 4 · (1 mm)² = 0.785 mm²
```

```
Marker area = π / 4 · (20 mm)² = 314.159 mm²
```

The marker area is 400 times larger. What does this imply? If the marker area is 400 times greater than the needle, you can can see that you'll need a force 400 times larger with the marker in order to pierce your skin. And that's basically why ear piercers and surgeons use slender surfaces are used to pierce/cut skin.

## Commonly Used Pressure and Stress Units

Pressure measurements are very much present in our daily lives:

- Our car tires' pressure is usually expressed in bars (bar) or pounds per square inch (psi).
- Medical scenarios frequently involve blood pressure measurements in millimeters of mercury (mmHg).
- Meteorologists lean towards hectopascals (hPa) or milibars (mb) when communicating atmospheric pressure in weather forecasts.
- In aviation, pressure is given in terms of altitude in feet above sea level.

Nevertheless, the International System (SI) uses a different unit for pressure quantities: the pascal (Pa).

The pascal (Pa) can be relatively small for certain engineering and scientific contexts, like in strength of materials. Given the notable differences in magnitudes, professionals often prefer to use kilopascals (kPa), megapascals (MPa), or gigapascals (GPa) to effectively communicate magnitudes in different situations.

When it comes to US units (imperial units), pounds per square inch (psi) or pounds per square foot (psf) are the most prevalent.

## How to Convert Pressure from Metric to US Units: MPa to psi

When we dive into converting pressure units, we find that pressure relies on three fundamental quantities: mass, length, and time. Time is universally measured in seconds, but different systems use different units for mass and length.

To understand how this conversion works, we need to go back to historical agreements that set up conversion factors for fundamental units. One significant agreement is the International Yard and Pound Agreement of 1959. This pact standardized how the foot (ft) relates to the metric system. According to this agreement:

```
ft = 0.3048 m
lb = 0.45359237 kg
```

Using these known conversions, we can work out a new factor for converting MPa (metric unit) into psi (Us unit).

First we need the conversion inches-meters:

```
ft = 12 in
in = 0.3048 / 12 m = 0.0254 m
```

Then, from the definition of pressure (force / area) and force (mass · acceleration):

```
psi = lbf / in²
= (lb · gravity) / in²
= (0.45359237 kg · 9.80665 m/s²) / (0.0254 m)²
= 0.45359237 · 9.80665 / 0.0254² Pa
= 6894.757293168361 Pa
= 6894.757293168361 Pa · (MPa / 1000000 Pa)
= 0.006894757293168361 MPa
```

Now, let's make things even clearer. We can divide both sides of the equation by `0.006894757293168361 MPa`

:

```
psi / (0.006894757293168361 MPa) = 1
```

This simple trick allows us to take the left side of the equation as a conversion factor. Applying this conversion factor to a pressure in MPa, the metric units cancel out, and we're left with the US unit we're aiming for: psi.

Here's an example of how to convert a pressure of 30 MPa into psi US units:

```
30 MPa · conversion_factor
= 30 MPa · psi / (0.006894757293168361 MPa)
= 30 / 0.006894757293168361 psi
= 4351.132131906277 psi
```

Let's round it to six decimals:

```
30 MPa = 4351.132132 psi
```

## How to Convert Pressure from US Units to Metric: psi to MPa

Using the same procedure, we can convert psi to MPa. We just have to invert the fraction to have in the denominator the units we need to cancel out:

```
0.006894757293168361 MPa / psi = 1
```

Here's how to convert a pressure of 5000 psi into metric units:

```
5000 psi · conversion_factor
= 5000 psi · (0.006894757293168361 MPa) / psi
= 5000 · 0.006894757293168361 MPa
= 34.473786 MPa
```

## Common Pressure Values

Reference | bar | MPa | psi |
---|---|---|---|

Blood pressure (systolic) | 0.15 | 0.015 | 2.1 |

Blood pressure (Diastolic) | 0.09 | 0.009 | 1.4 |

Atmospheric pressure | 1.01 | 0.101 | 14.7 |

Pressure 100 m under water | 11 | 1.1 | 160 |

Car tires pressure | 2.5 | 0.25 | 36 |

Truck tires pressure | 8 | 0.8 | 36 |

Aircraft tires pressure | 14 | 1.4 | 200 |

## Common Materials Strength Values

Reference | MPa | psi |
---|---|---|

Soft soil shear strength | 0.03 | 5 |

Hard soil shear strength | 0.20 | 30 |

Concrete tensile strength | 3.4 | 500 |

Concrete compression strength | 34 | 5000 |

Reinforcing steel tensile strength | 517 | 75000 |

## Explore More

Here're some additional resources to deepen into the topic:

- Check out some worked examples of how pressure conversion factors can be derived: MPa to psi, psi to MPa, psf to psi, and psi to psf.