Force conversion factor from lbf to N

Analyzing lbf and N Units

In this article, we'll explore force units and calculate the conversion factor from lbf to N.

• lbf stands for pound-force, and is a common US unit for force. It's often informally referred to as pound or lb, although not entirely accurate.
• N stands for newton, and is the fundamental unit of force in the International System (SI).

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

Force = mass · acceleration
      = mass · speed / time
      = mass · length / time²

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 Force from US Units to Metric: lbf to N

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 lbf (US unit) into N (metric unit).

It's worth noting that there are differences in the definitions of pounds-force and newtons. Pounds-force depends on the gravitational acceleration:

lbf = mass · gravity
    = lb · 9.80665 m/s²
    = lb · 9.80665 m/s² · (1 ft) / (0.3048 m)
    = 9.80665/0.3048 lb ft/s²
    ≈ 32.174049 lb ft/s²

On the other hand, the newton unit relies solely on other SI units, independent of the gravitational acceleration:

N = mass · acceleration
  = kg · m/s²

Now, let's express N in terms of US units of mass and acceleration:

N = kg · acceleration
  = 1/0.45359237 lb · m/s²
  = 1/0.45359237 lb · m/s² · (ft) / (0.3048 m)
  = 1 / (0.45359237 · 0.3048) lb ft/s²

Given the definition of lbf shown earlier:

lb ft/s² = 0.3048 / 9.80665 lbf

Then, we can substitute:

N = 1 / (0.45359237 · 0.3048) lb ft/s²
  = 1 / (0.45359237 · 0.3048) · 0.3048 / 9.80665 lbf
  = 1 / (0.45359237 · 9.80665) lbf
  ≈ 0.22480894309971047 lbf

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

N / (1 / (0.45359237 · 9.80665) lbf) = 1

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

factor = N / (1 / (0.45359237 · 9.80665) lbf)
       = (0.45359237 · 9.80665) N / lbf
       ≈ 4.4482216152605 N / lbf

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

Convert 70 lbf to N

Here's an example of how to convert a pressure of 70 lbf into N:

70 lbf · factor
= 70 lbf · 4.4482216152605 N / lbf
= 70 · 4.4482216152605 N
= 311.375513068235 N

lbf to N Conversion Factor

Here're the resulting key takeaways.

1 N ≈ 0.22480894309971047 lbf

Converting a lbf unit into N is as simple as multiplying it by a conversion factor:

N = lbf · factor

where factor is exactly:

factor = (0.45359237 · 9.80665)

or approximately:

factor = 4.4482216152605

Explore More

Here are some additional resources to deepen into this topic:

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