# Pressure conversion factor from MPa to psi

## Analyzing MPa and psi Units

In this article, we'll explore pressure units and calculate the conversion factor from MPa to psi.

- MPa, short for megapascal, is a metric unit equivalent to one million pascals (Pa). Pascal is the fundamental unit of pressure in the International System (SI).
- psi stands for pound-force per square inch, and is a common US unit for pressure. It's often informally referred to as pounds per square inch, although not entirely accurate.

As we delve into converting pressure units, we'll see that pressure relies on three fundamental quantities: mass, length, and time:

```
Pressure = force / area
= mass · acceleration / area
= mass · speed / time / area
= mass · length / time² / length²
= mass / time² / length
```

While time is consistently measured in seconds in both metric and US units, we'll need to address the differences in mass and length units, which is where our journey begins.

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

To understand the conversion process, let's go back to historical agreements that set up conversion factors for fundamental units. One pivotal agreement is the International Yard and Pound Agreement of 1959. This pact standardized how the pound (lb) and the foot (ft) relate to the metric system. According to this agreement:

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

With these established conversions, we can derive a new factor for converting MPa (metric unit) into psi (a US unit).

First we need the equivalence between inches and meters:

```
ft = 12 in
in = 1 ft / 12
= 0.3048 m / 12
= 0.0254 m
```

Additionally, we'll require the gravitational acceleration in metric units:

```
gravity = 9.80665 m/s²
```

Now we have all we need to derive the relationship between MPa and psi. Starting with the definition of pressure (force / area) and force in terms of pound-force (mass · gravity, check out this article for more details):

```
psi = lbf / in²
= (lb · gravity) / in²
= (0.45359237 kg · 9.80665 m/s²) / (0.0254 m)²
= 0.45359237 · 9.80665 / 0.0254² Pa
= 0.45359237 · 9.80665 / 0.0254² Pa · (MPa / 1e6 Pa)
= 0.45359237 · 9.80665 / (0.0254² · 1e6) MPa
≈ 0.006894757293168361 MPa
```

Now, let's make things even clearer. We can divide both sides of the equation by `0.45359237 · 9.80665 / (0.0254² · 1e6) MPa`

:

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

This manipulation provides us with the left side of the equation as a convenient conversion factor.

```
factor = psi / (0.45359237 · 9.80665 / (0.0254² · 1e6) MPa)
= (0.0254² · 1e6) / (0.45359237 · 9.80665) psi / MPa
≈ 145.03773773020922 psi / MPa
```

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.

## Convert 30 MPa to psi

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

```
30 MPa · factor
= 30 MPa · 145.03773773020922 psi / MPa
= 30 · 145.03773773020922 psi
= 4351.132131906277 psi
```

## MPa to psi Conversion Factor

Here're the resulting key takeaways.

```
1 psi ≈ 0.006894757293168361 MPa
```

Converting an MPa unit into psi is as simple as multiplying it by a conversion factor:

```
psi = MPa · factor
```

where factor is exactly:

```
factor = (0.0254² · 1e6) / (0.45359237 · 9.80665)
```

or approximately:

```
factor ≈ 145.03773773020922
```

## Explore More

Here are some additional resources to deepen into the topic:

- Convert Pressure Units with this Converter.
- Check out other worked examples of how pressure conversion factors can be derived: psi to MPa, psi to psf, psf to psi, psi to ksi, or ksf to MPa.
- Check out other worked examples of how force conversion factors can be derived: lbf to N, kN to lbf, or lbf to kN.