There are common mistakes people make in physics and engineering courses when using a calculator. This page will explain how to avoid them.

Squaring a Negative Number

TLDR: Always include parenthesis around a negative number before squaring it, like this: 0.5*300*(-5)2.

Equations that require squaring a number usually look something like this:

KE = \frac{1}{2}mv^2

Note that there are no parenthesis surrounding the variable being squared, the equation does not look like this:

KE = \frac{1}{2}m(v)^2

When the velocity value is negative, students typically enter the calculation into their calculator as follows (given a mass of 300 kg and velocity of -5 m/s2):

TI-83 Plus with the following input: .5*300*-5^2 and the output of: -3750

This results in a negative answer (-3,750 J), which is incorrect. The square of a negative number is always positive. Your calculator is interpreting the negative sign on the velocity as this:

KE = \frac{1}{2}m(-(v^2))

What should you do instead? Any time you need to square a negative number, include parenthesis around the negative number before squaring it! This is how it should look on your calculator:

TI-83 Plus with the following input: .5*300*(-5)^2 and the output of: 3750

This tells your calculator specifically to square the negative number and will give you a correct result (in this case, 3,750 J).

Dividing by Multiplied Values

TLDR: Always include your denominator in parenthesis, like this: 1/(4*π).

Sometimes, you need to divide by two values multiplied together. Consider the equation for the wavelength of a matter wave:

\lambda = \frac{h}{mv}

Note that there are no explicit parenthesis around the denominator, the equation does not look like this:

\lambda = \frac{h}{(mv)}

Students may enter this equation into their calculator like this (given a mass of 300 kg and velocity of 5 m/s2):

TI-83 Plus with the following input: 6.626E-34/300*5 and the output of: 1.10433333E-35

This results in the wrong value (1.1 x 10-35 m)! Your calculator is performing h/m, and then multiplying by v, like this:

\lambda = \frac{h}{m}*v

What should you do instead? Always put parenthesis around your denominator to instruct your calculator to perform the correct order of operations! This is how it should look on your calculator:

TI-83 Plus with the following input: 6.626E-34/(300*5) and the output of: 4.41733333E-37

Now your calculator will give you the correct value (4.4 x 10-37 m), because the calculator first multiplied mass and velocity, and then divided Planck’s constant (h) by that multiplied value.

Powers of Ten

TLDR: Always use E, only use it once, and don’t include it with any other power of ten calculation, like this: 6.67E-11

Lots of physical parameters are really big or really small and use scientific notation. Entering this into a calculator can just be tricky.

Scientific notation looks like this:

G = 6.67 \times 10^{-11}~\textrm{Nm}^2/\textrm{kg}^2

The entire “\times 10^{}” (“times ten to the power of…”) can be entered into your calculator using the EE button (usually requiring a shift key, so look above the buttons to find it). Here’s how you should input this into your calculator:

TI-83 Plus with the following input: 6.67E-11 and the output of: 6.67E-11

Sometimes students don’t realize that the EE button multiplies by ten and may do something like this instead, which results in an incorrect value for the physical parameter:

TI-83 Plus with the following input: 6.67*10E-11 and the output of: 6.67E-10

Note that the output of the calculator even shows that the result is incorrect; it’s saying it thinks the result is 6.67E-10, or 6.67 \times 10^{-10}.

To check your result, the output of your calculator should be the same value that you typed in! If it’s any different, then make sure you used the EE button correctly.