Pressure conversion factor from psi to MPa

Analyzing psi and MPa Units

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

• 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.
• 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).

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 US Units to Metric: psi to MPa

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 psi (US unit) into MPa (metric unit).

First we need the equivalence between inches and meters:

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

Now we have all we need to derive the relationship between psi and MPa. Starting with the definition of pressure (force / area) and force (mass · acceleration):

MPa = 1e6 Pa
    = 1e6 N / m² 
    = 1e6 (kg · m/s²) / m² 
    = 1e6 · 1/0.45359237 lb · ft/s²/(0.3048 m)  / (1/0.0254 in)²
    = 1e6 · 0.0254² / (0.45359237 · 0.3048) · lb · ft/s² / in²

Given the definition of lbf or pound-force (check out this article for more details):

lbf = lb · 9.80665 m/s² · ft / (0.3048 m)
    = 9.080665 / 0.3048 lb ft/s²

lb ft/s² = 0.3048 / 9.80665 lbf

Then, we can substitute:

MPa = 1e6 · 0.0254² / (0.45359237 · 0.3048) · lb · ft/s² / in²
    = 1e6 · 0.0254² / (0.45359237 · 9.80665) lbf / in²
    = 1e6 · 0.0254² / (0.45359237 · 9.80665) psi
    ≈ 145.03773773020922 psi

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

MPa / (1e6 · 0.0254² / (0.45359237 · 9.80665) psi) = 1

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

factor = MPa / (1e6 · 0.0254² / (0.45359237 · 9.80665) psi)
       = (0.45359237 · 9.80665) / (1e6 · 0.0254²) MPa / psi
       ≈ 0.006894757293168362 MPa / psi

Applying this conversion factor to a pressure in psi, the US units cancel out, and we're left with the metric unit we're aiming for: MPa.

Convert 5000 psi to MPa

Here's an example of how to convert a pressure of 5000 psi into MPa:

5000 psi · factor
= 5000 psi · 0.006894757293168362 MPa / psi
= 5000 · 0.006894757293168362 MPa
= 34.473786465841805 MPa

psi to MPa Conversion Factor

Here're the resulting key takeaways.

1 MPa ≈ 145.03773773020922 psi

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

MPa = psi · factor

where factor is exactly:

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

or approximately:

factor ≈ 0.006894757293168362

Explore More

Here are some additional resources to deepen into this topic:

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