# Scientific Calculator

### About Scientific Calculator

This free, easy-to-use scientific calculator can be used for any of your calculation needs but it is specialized for usage by engineers and scientists. With the inclusion of many different features, easy access to a wide variety of scientific constants. This calculator is optimized for either desktop or mobile use, making it a portable powerhouse or a reliable at-the-desk tool.

**Basic operations:** Even the most advanced scientific calculator needs the basics in order to be useful - here are the most commonly used and basic functions:

**Addition:**

(x + y) Addition, also known as summing or, more colloquially, “plus” is used to sum numbers together.

**Subtraction:**

(x - y) Subtraction, the “minus” sign, or sometimes difference, is used to find the numerical separation between two numbers, thus the term “difference”.

**Multiplication:**

(x * y) Multiplication, the product or “times” is represented sometimes by an “x” and sometimes by an asterisk “*”.

**Division:**

(x / y) Division, sometimes referred to as the quotient, is sometimes shown as a fraction, a “/” or the “÷” symbol. Which is supposedly called an “obelus” - who knew?

**Trigonometric functions:** In mathematics and in various fields of engineering, trigonometric functions are frequently used to solve different problems. It could be as simple as solving an unknown value of a right-angled triangle or solving the instantaneous power absorbed by an electrical element. Here are the trigonometric functions that you will encounter as you study mathematics and engineering:

**Sine**

In a right-angled triangle, the sine function can be used to relate the angle to the ratio of the length of the side opposite the angle and the hypotenuse. The sine function can be used in this scientific calculator by clicking the “sin” button.

**Cosecant**

The cosecant function is a reciprocal of the sine function.

**Cosine**

The cosine function is another trigonometric function that can be used to relate the angle of a right triangle to the ratio of the length of the side adjacent to the angle and the hypotenuse. It can be used in this scientific calculator by clicking the “cos” button.

**Secant**

The secant function is a reciprocal of the cosine function.

**Tangent**

The tangent function relates the angle of a right-angled triangle to the ratio of the length of the side opposite the angle and the side adjacent to the angle. This function can be used in this scientific calculator by clicking the “tan” button.

**Cotangent**

The cotangent function is a reciprocal of the tangent function.

**Inverse Sine**

The inverse sine (arcsine) trigonometric function can be used to determine the angle of a sine value. This can be used in this scientific calculator by clicking the “asin” button. The domain of an inverse sine function is from -1 to +1 and the range is from -90° to +90°.

**Inverse Cosine**

The inverse cosine (arccosine) trigonometric function can be used to determine the angle of a cosine value. To use this function, just click the “acos” button of this scientific calculator. The domain of the arccosine function is just the same with the arcsine function but its range is from 0 to +180°.

**Inverse Tangent**

The inverse tangent (arctangent) trigonometric function can be used to determine the angle of a tangent value from a domain covering all real numbers. The range of the arctangent function is from -90° to +90°. To use this function, click the “atan” button of this scientific calculator.

**Other Functions:**

**Imaginary Unit**

Whenever you multiply a negative number with a negative number, the result is a positive number. Specifically, any number squared will be a positive number, as it’ll either be a positive number multiplied by itself, yielding another positive number, or a negative number multiplied by itself, again yielding a positive number. Yet sometimes, you need something that, somehow, when multiplied by itself, gives a negative number. Mathematicians have called this number “*i*”, wherein (*i*^{2} = -1) To avoid confusion with the symbol for electrical current, in electrical engineering we frequently use “j” instead of “*i*”. In the calculator, simply use it as you would any other number, though you can’t use your keyboard to put it in - click on the bolded “i” box instead.

**Factorial**

Factorials are odd beasts that don’t show up very frequently but are important when you need them. Factorial is where you take a positive number, multiply it by the next smaller whole number, then multiply it by the next smaller whole number, until you reach one. Mathematically, it looks like this:

n! = n * (n - 1) * (n - 2) * ... 2 * 1

This is based purely off of personal experience, but we tend to see factorials in summation and series problems - those epsilon summation problems in calculus where you’re approximating differentials or integrals with series. But the strangest thing to us about factorials is that (0! = 1) - weird, eh?

**Natural Logarithm**

A natural logarithm is simply a logarithm but with a specific base, the number “*e*” which is around 2.72 (you can get the whole constant using the constants tool at the top of the calculator). To understand natural logarithms, though, you need to remember that a logarithm is basically the inverse of an exponent.

log_{x}(y) = z is another way of saying x^{z} = y

Using the base of *e*, you’re assuming that the base (x in this example) is “*e*”:

So ln(y) = z is the same as log_{e}(y) = z

A few important properties to remember:

With a natural log, (ln(1) = 0)

This is because (log_{e}(*1*) = 0) is just another way of saying (*e*^{0} = *1*)

But with (ln(*e)* = 1), the base and argument are then both “e”, so we get:

log_{e}(*e*) = 1 or (*e*^{1} = *e)*

We could get lost going deep with logarithms and natural logarithms but we’ll stop here and hopefully that’s enough to help you get started if you had any questions.

**Natural Exponential**

The function ex is known as the natural exponential function which has inverse functions such as natural logarithm (ln), or logarithm to base e [log_{e} (x)]. The number “e”, which is sometimes called Euler's number, is a mathematical constant that is the base of the natural logarithm. It is one of the most frequently used numbers in mathematics together with 0, 1, pi, and i. Euler's number is approximately equal to 2.718281828. So using the natural exponential function is like raising the number 2.718281828 to the power of “x”. To use this function, click the e^x button and input the number that would represent “x”. Then click “=” for the result.

**Raise to the Power**

The y^{x} is a function that raises a number “y” to the power of a number “x”. For example, let “y” be equal to 2 and “x” be equal to 3. Replacing the variables with the actual numbers, then it would be 2^{3}, which is equal to 8. To use this function, input a number first that would represent “y” and click the “y^{x}“ button. Then input a number that would represent “x” and hit the “=” button for the result.

**Inverse**

The multiplicative inverse or reciprocal function, denoted by 1/x, gets the reciprocal of a number “x”. It could also be represented as x-1. To use this function in the scientific calculator, input first a number and click the “1/x” button. Then click the “=” button for the result.

**Square**

The x^2 is function that simply raises a number “x” to the power of 2 or multiplies the number by itself. For example, squaring a number 4, that would be 4^2 or 4x4 which is equal to 16. To use this function in the scientific calculator, input a number to be squared and click the x^2 button. Then click = button for the result.

**Logarithm**

The logarithm of a number “x” is the exponent “y” of the base “b” of the logarithm that would produce the number “x”. For example, if the base “b” is 10 and the number “x” is 10000, so log_10 (10000) = 4. To prove this, let’s raise the base 10 to the power of 4, and yes, 10^4 is equal to 10000.

Similar to as we talked about above under natural logarithms:

(log_{b}(x) = y) is a different way to say (b^{y} = x)

Or, as with this example:

log_{10}(10000) = 4 or 10^{4} = 10000

To use the logarithm function of this scientific calculator, click the “LOG” button and input the number. Then click the = button for the result. The “LOG” function in this calculator is a common logarithm. The base is fixed to 10.

**Scientific Notation**

The scientific notation or “EE” button helps in inputting very large or very small numbers. For example, we’re going to add 2500000 and 1500000, instead of inputting 2,500,000+1,500,000, we can just input 2.5E6+1.5E6 and click the = button to get the result. The E represents “x10^x”.

**Negative Sign**

The negative sign button (-) can be used to change the sign of the number. To use this, click the “-” button first and input the number.

**Polar Angle Symbol**

When dealing with phasors, the complex number can be represented in a polar form. The polar angle symbol “∠” can be used to indicate the angle.

**Square Root**

A square root is a number that when multiplied by itself produces a square. For example, 3 is the square root of 9 since when 3 is multiplied by itself, 3, produces a square of 9. To find the square root of a number using this scientific calculator, simply click the √ button, input the number, and click the = button to get the result.

**Clear Button**

The letter “C” denotes clear, which will clear all current input and memory of previous actions. If you wish to use the previous answer in your next calculation, do not use this button. It will not only clear the numbers and symbols you’ve put in for your current calculation but will also clear the answer cache. However, if you want to make sure that your calculations aren’t somehow getting remnants of previous calculations unintentionally, this is a good way to do that.

**Delete Button**

If you’ve mistyped something and want to delete only your most recent input, use the delete button, which is denoted with the leftward facing arrow with the “X” in it. This will not erase the memory and will only erase one character at a time. However, it will delete from the most recently inputted character to the oldest inputted character.

**Answer Button**

The Answer button (Ans) is if you wish to use the answer to the previous calculation in your current calculation, you can either start your calculations immediately with an operator (plus, minus, etc.) and the previous answer will be inserted automatically, or you can manually click the “Ans” button to put the value anywhere in the equation you’d like.

**Degree/Radian Button**

To switch between degrees and radians within the calculator, simply click in the top left of the calculator where it says either “DEG” or “RAD” and it will toggle between the two. They both have their strengths and weaknesses but when working with sinusoidal signals (such as AC signals), radians is typically the format of choice.

**Rectangular/Polar Button**

Sometimes you want to use rectangular notation and other times you wish to use polar notation. We get it. To switch between the two, where it either says REC (rectangular, or degrees) or POL (polar, or radians) in the upper left hand corner, just tap or click that to toggle between the two modes.

**Constants**

We’ve created a constant library to save you time from looking up constants and typing them in manually! Just click Constants in the upper right hand corner next to the “π” symbol. You can either scroll down and find the constant manually or use the search bar at the top to pull up the constant you’re looking for. Ironically, these constants aren’t constant - if you have any ideas for constants we’re missing, let us know and we can add them!