Convert Force Units

Force Dimensional Analysis

The dimensional analysis stems from the interrelation of two other quantities: mass and acceleration.

Force = mass · acceleration
      = M¹ L¹ / T²
      = M¹ L¹ T⁻²

Commonly Used Force Units

Force measurements aren't commonly used on everyday life. When discussin weights, we tend to refer to mass measurements, even though weight is fundamentally a force. Outside of this context, you'll rarely come across units like newtons or pounds-force.

However, in scientific and engineering domains, force measurements are extensively used across multiple disciplines. There're multiple types of forces, such as: gravitational forces, electromagnetic forces, normal forces, friction forces, or centripetal forces.

Within the International System (SI), the unit for measuring force is the newton (N). In specific engineering and scientific contexts, the newton (N) might seem relatively small. For instance, in civil structural engineering, professionals often find it more practical to express force magnitudes in kilonewtons (kN).

In the realm of US customary units (imperial units), the most relevant force units are pounds-force (lbf) and kilopound (kip), which is equal to 1000 lbf.

Understanding the Difference between Weight and Mass

Weight and mass concepts are often used incorrectly in everyday language:

I weight 180 pounds.

I weight 80 kilograms.

However, weight and mass have different meanings in physics:

• Mass refers to the amount of matter in an object. Mass remains constant regardless the object location in the universe. An object has the same mass in the Earth and in Jupyter.
• Weight, on the other hand, is the force exerted on an object due to gravity. It depends on the object mass and the gravitational field. Given that the gravity in Jupyter is larger than in Earth, the weight of the same object is greater in Jupyter than in Earth.

Let's explore an example of a 100-pounds object, comparing the weight in Earth and Jupyter:

Weight in Earth = 100 lb · 32.1740 ft/s²
                = 3217.4 lbf

Weight in Jupyter = 100 lb · 80 ft/s²
                  = 8000 lbf

We see that the weight of the very same object in Jupyter is around 2.5 times greater than in Earth, even though the object mass remains constant.

Once the concepts of weight and mass have been clarified, let's come back to the initial everyday expressions. Here're the physically correct sentences we should use instead:

I weight 5796 pounds-force (on Earth).

My mass is 180 pounds.

Or using the metric system:

I weight 785 newtons (on Earth).

My mass is 80 kilograms.

How to Convert Force from Metric to US Units: kN to lbf

When we dive into converting force units, we find that force 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 from metric kilonewton (kN) into puonds-force (lbf) US unit.

lbf = lb · gravity
    = 0.45359237 kg · 9.80665 m/s²
    = 0.45359237 · 9.80665 N 
    = 4.4482216152605 N
    = 4.4482216152605 N · (kN / 1000 N)
    = 0.0044482216152605 kN

Now, let's make things even clearer. We can divide both sides of the equation by 0.0044482216152605 kN:

lbf / (0.0044482216152605 kN) = 1

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

Here's an example of how to convert a force of 30 kN into US units (pounds-force, lbf):

30 kN · conversion_factor
= 30 kN · lbf / (0.0044482216152605 kN)
= 30 / 0.0044482216152605 lbf
= 6744.268292991315 lbf

Let's round it to six decimals:

30 kN = 6744.268293 lbf

How to Convert Force from US Units to Metric: lbf to kN

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

0.0044482216152605 kN / lbf = 1

Here's how to convert a force of 5000 lbf into kN metric units:

6000 lbf · conversion_factor
= 6000 lbf  · (0.0044482216152605 kN) / lbf
= 6000 · 0.0044482216152605 kN
= 26.689330 kN

Common Weights in Nature

Here you'll find a list of weight references to effectively compare orders of magnitude. Remember the difference between weight and mass: weight is a force, measured in newtons (N) or pounds-force (lbf), while mass is measured in kilograms (kg) or pounds (lb). We're including both weight and mass in the following examples.

Common Vehicle Weights

Like in the previous section, this table shows some common vehicle weights. But here we're using kilonewtons (kN) and kilopounds (kips) instead of newtons (N) and pounds-force (lbf) for convenience.

Explore More

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

• Check out some worked examples of how force conversion factors can be derived: N to lbf, lbf to N, kN to lbf, and lbf to kN.