# Clearing up Unit Confusion with PTC Mathcad

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Converting between two unit systems or converting within a single unit system is expected to be done flawlessly. The reality is, mistakes happen. Common conversions like inches (in) to centimeters (cm), or miles (mi) to feet (ft) may be memorized, but the conversion factor between pound force per square inch (psi) and Pascals (Pa) is likely searched on Google and manually entered into a calculation. With PTC Mathcad Prime 3.1, you will never have to look up a unit conversion factor again or worry that you may have made a mistake doing a conversion. The only confusion left will be why the United States has not adopted the metric system.

Sir Isaac Newton’s 2nd law of motion states the net force on an object is equal to the mass of the object multiplied by the acceleration of the object. This law holds true for all constant mass systems. The International System of Unit (metric system) defines force in terms of the Newton (N) and mass in terms of the kilogram (kg). The United States Customary System of Units (USCS system) defines force in terms of the pound-force (lbf) and mass in terms of the pound (lb or lbm) or the slug (slug). These are the unit definitions and abbreviations that PTC Mathcad Prime 3.1 uses. So, you’re telling me that in the metric system 1* 9.8 = 9.8, but in the USCS system, 1 * 32 = 1. How in the world does 1 * 32 = 1?

In the metric system, 1 Newton is defined as the force required to accelerate 1 kilogram (of mass) at 1 meter per second squared. So to accelerate 1 kilogram at 9.8 meters per second, a 9.8 Newton force would be required as we see in the above calculation. In the USCS system, 1 pound-force is defined as the force required to accelerate 1 pound (of mass) at 32.2 feet per second squared which is why 1 *32 = 1 in the above calculation. The slug is another unit of mass in the USCS system which is equivalent to 32.2 pounds (of mass).

Using the slug as the unit of mass in the USCS system gives us the 1 = 1 * 1 that we expected to see.

Now that we understand how PTC Mathcad Prime 3.1 defines units of mass and force in the USCS system, lets see how getting pound and pound force confused can throw off your Mathcad Prime 3.1 worksheet. One common error users make is defining a force in terms of lb, which as we discussed above, is a unit of mass in PTC Mathcad, not force. Below you will notice how that simple mistake can throw off your units when calculating for parameters like pressure, stress, and power.

As you can see above, forgetting to add the f in lbf can cause your units to be incorrect. Therefore, when using the USCS system for calculating parameters like stress, pressure, and power, be sure to use lbf and not lb.

As long as you define your units with the correct abbreviations, PTC Mathcad Prime 3.1 will automatically perform unit conversion flawlessly, saving you time and effort on all of your calculations and eliminating all errors, big or small.

Visit the dedicated unit conversion feature page.