How to Use a Scientific Calculator (Functions)

A scientific calculator does far more than basic arithmetic. It handles trigonometry, logarithms, exponents, roots, factorials, and constants like pi and e. Understanding what each function does and when to use it turns an intimidating grid of buttons into a powerful problem-solving tool.

This guide covers every major function you will encounter, from order of operations to memory storage. Try each example yourself using our Scientific Calculator to build confidence.

Order of Operations: PEMDAS / BODMAS

Before using any advanced function, you must understand how calculators evaluate expressions. Scientific calculators follow a strict hierarchy:

1. Parentheses (Brackets)
2. Exponents (Orders)
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

This means 2 + 3 x 4 equals 14, not 20. The calculator multiplies 3 x 4 = 12 first, then adds 2.

Common mistake: Entering 100 / 4 + 1 when you mean 100 / (4 + 1). The first gives 26, the second gives 20. Parentheses are your best friend — use them liberally to make your intent explicit.

Nested Parentheses

Calculators handle multiple layers of parentheses from the inside out:

$((5 + 3) \times 2)^2 = (8 \times 2)^2 = 16^2 = \mathbf{256}$

If you lose track of open parentheses, most scientific calculators display a count or highlight unmatched brackets.

Trigonometric Functions: sin, cos, tan

Trigonometry is the core reason most people reach for a scientific calculator. The three primary functions relate the angles and sides of right triangles.

• sin(angle) = opposite side / hypotenuse
• cos(angle) = adjacent side / hypotenuse
• tan(angle) = opposite side / adjacent side

Degree vs. Radian Mode

This is the single most common source of wrong answers. Before entering any trig calculation, check your mode:

Mode	Full Circle	Right Angle	When to Use
Degrees	360	90	Most everyday problems, construction, navigation
Radians	2pi	pi/2	Calculus, physics, engineering formulas

Test: Enter sin(90). If the answer is 1, you’re in degree mode. If it’s approximately 0.894, you’re in radian mode.

Inverse Trig Functions

The inverse functions (sin^-1, cos^-1, tan^-1) work backward — given a ratio, they return the angle.

Example: A ladder leans against a wall. The base is 5 feet from the wall and the ladder reaches 12 feet up. What angle does the ladder make with the ground?

$\theta = \tan^{-1}\left(\frac{12}{5}\right) = \tan^{-1}(2.4) = \mathbf{67.38\degree}$

Worked Example: Finding a Roof Pitch

A roof rises 6 inches for every 12 inches of horizontal run. The pitch angle:

$\theta = \tan^{-1}\left(\frac{6}{12}\right) = \tan^{-1}(0.5) = \mathbf{26.57\degree}$

Logarithms: log and ln

A logarithm answers the question: “What exponent gives me this number?”

• log(x) = base-10 logarithm. log(1000) = 3 because 10^3 = 1000.
• ln(x) = natural logarithm (base e, where e = 2.71828…). ln(e) = 1.

When to Use Each

Function	Common Applications
log (base 10)	Decibels, pH chemistry, Richter scale, signal processing
ln (base e)	Compound interest, population growth, calculus, half-life decay

Practical Examples

Decibel calculation: A sound is 1,000 times more intense than the reference level. How many decibels?

$dB = 10 \times \log(1000) = 10 \times 3 = \mathbf{30 \ dB}$

Doubling time: An investment grows at 7% annual interest compounded continuously. How long to double?

$t = \frac{\ln(2)}{0.07} = \frac{0.6931}{0.07} = \mathbf{9.9 \ years}$

Change of Base Formula

Need a logarithm with a base other than 10 or e? Use:

$\log_b(x) = \frac{\log(x)}{\log(b)}$

Example: log base 2 of 64:

$\log_2(64) = \frac{\log(64)}{\log(2)} = \frac{1.806}{0.301} = \mathbf{6}$

This confirms that 2^6 = 64.

Exponents and Roots

The Power Key (^ or x^y)

Enter the base, press the exponent key, then enter the power.

• 2 ^ 10 = 1,024
• 1.05 ^ 30 = 4.3219 (compound growth of 5% over 30 periods)

Square Root and nth Root

• sqrt gives the square root: sqrt(144) = 12
• For cube roots, use x ^ (1/3): 27^(1/3) = 3
• For any nth root, use x ^ (1/n): 625^(1/4) = 5

Physics example: The period of a pendulum is:

$T = 2\pi\sqrt{\frac{L}{g}}$

For a 1-meter pendulum with g = 9.81 m/s^2:

$T = 2 \times \pi \times \sqrt{\frac{1}{9.81}} = 2 \times 3.14159 \times 0.31928 = \mathbf{2.006 \ seconds}$

Pi and e Constants

Most scientific calculators have dedicated keys for these two fundamental constants:

• pi = 3.14159265… Used in circles, spheres, waves, and periodic functions.
• e = 2.71828182… The base of natural logarithms, central to growth and decay formulas.

Circle area: A circular patio has a 6-foot radius.

$A = \pi r^2 = \pi \times 36 = \mathbf{113.10 \ sq \ ft}$

Continuous compounding: $1,000 at 5% for 10 years:

$A = 1000 \times e^{(0.05 \times 10)} = 1000 \times e^{0.5} = 1000 \times 1.6487 = \mathbf{\$1,648.72}$

Parentheses: Avoiding Common Errors

The number one cause of wrong answers is missing parentheses. Here are five expressions where they matter:

Intended Calculation	Correct Entry	Wrong Entry	Wrong Result
Fraction: (3+4)/(2+5)	(3+4)/(2+5) = 1	3+4/2+5 = 10	Off by 9
Negative exponent: 2^(-3)	2^(-3) = 0.125	2^-3 = error or -8	Completely wrong
Trig of expression: sin(30+15)	sin(30+15) = sin(45)	sin(30)+15 = 15.5	Off by 14.79
Compound fraction: 1/(1+r)^n	1/(1+0.05)^10	1/1+0.05^10	Way off
Nested root: sqrt(a^2+b^2)	sqrt(3^2+4^2) = 5	sqrt(3)^2+4^2 = 19	Off by 14

When in doubt, add more parentheses. Extra parentheses never produce a wrong answer; missing ones frequently do.

Memory Functions: M+, M-, MR, MC

Memory keys let you store intermediate results without writing them down.

• M+ adds the displayed number to memory.
• M- subtracts the displayed number from memory.
• MR (Memory Recall) displays the stored value.
• MC (Memory Clear) resets memory to zero.

Example workflow: Calculate the total cost of three items with different tax rates.

1. Item 1: 25.00 x 1.08 = 27.00. Press M+.
2. Item 2: 42.50 x 1.06 = 45.05. Press M+.
3. Item 3: 18.75 x 1.09 = 20.44. Press M+.
4. Press MR to see the total: 92.49.

The ANS key on many calculators recalls the most recent result, which is useful for chaining calculations. For example, calculate a value, then immediately enter ANS x 1.08 to add 8% tax.

The Factorial Function (n!)

The factorial of n is the product of all positive integers from 1 to n.

$5! = 5 \times 4 \times 3 \times 2 \times 1 = \mathbf{120}$

Factorials appear in probability and combinatorics. The number of ways to arrange 8 books on a shelf is 8! = 40,320.

Combination formula (choosing r items from n):

$C(n, r) = \frac{n!}{r!(n-r)!}$

How many 5-card poker hands from a 52-card deck?

$C(52, 5) = \frac{52!}{5! \times 47!} = \mathbf{2,598,960}$

Frequently Asked Questions

What is the difference between the negative sign (-) and the subtraction key?

Most scientific calculators have two separate keys. The (-) or +/- key makes a number negative (e.g., entering -5). The minus key performs subtraction between two values. Using the wrong one is a common source of “syntax error” messages. If you need to enter a negative exponent like 2^(-3), use the negation key, not the subtraction key, inside the parentheses.

How do I switch between degrees and radians?

Look for a DRG or MODE button. Pressing it cycles through Degrees, Radians, and sometimes Gradians. On our Scientific Calculator, you can toggle the angle mode directly above the input area. Always verify your mode before starting trig calculations — a wrong mode setting is the number one reason students get incorrect trig answers on exams.

Can a scientific calculator handle complex numbers?

Many advanced scientific calculators support complex number arithmetic. You can enter values in the form a + bi and perform addition, subtraction, multiplication, and division. This is essential for electrical engineering calculations involving impedance and AC circuits. If your calculator doesn’t have a dedicated complex mode, you can manually compute the real and imaginary parts using the formulas for complex arithmetic.

How do I calculate a percentage on a scientific calculator?

Enter the number, multiply by the percentage value, then divide by 100. For 15% of 240: enter 240 x 15 / 100 = 36. Some calculators have a dedicated % key that automatically divides by 100. For percentage increase, multiply by (1 + rate): 240 x 1.15 = 276. For percentage decrease, multiply by (1 - rate): 240 x 0.85 = 204. For more percentage operations, try our Percentage Calculator.

Explore all of these functions hands-on with our Scientific Calculator — no download required.