How to Use a Scientific Calculator: Trig, Logs, Powers and Factorials

The short answer

A scientific calculator adds functions to basic arithmetic: trigonometry (sin, cos, tan and their inverses), logarithms (log and ln), powers and roots, factorials and constants like π and e. The most important setting is the angle mode: DEG for degrees, RAD for radians. The free Scientific Calculator shows the mode on screen and keeps your last ten calculations in a history list.

DEG vs RAD: the most common mistake

Angles can be measured in degrees (a full turn is 360°) or radians (a full turn is 2π, about 6.283). The calculator has to know which you mean:

• In DEG mode, sin(30) = 0.5.
• In RAD mode, sin(30) = −0.988, because it reads 30 as 30 radians.

School trigonometry and most practical problems use degrees. Calculus and physics formulas usually assume radians. If an answer looks wrong, check the mode first. The DEG/RAD button switches between them.

Trigonometry

sin, cos, tan

These relate an angle in a right-angled triangle to the ratios of its sides:

• sin = opposite ÷ hypotenuse
• cos = adjacent ÷ hypotenuse
• tan = opposite ÷ adjacent

Example: a ladder 5 m long leans at 60° to the ground. How high does it reach? Height = 5 × sin(60) = 5 × 0.866 = 4.33 m. Type 5×sin(60) in DEG mode.

Inverse functions: sin⁻¹, cos⁻¹, tan⁻¹

These go the other way: from a ratio back to an angle. In DEG mode the answer is in degrees.

• sin⁻¹(0.5) = 30
• cos⁻¹(0.5) = 60
• tan⁻¹(1) = 45

Example: a ramp rises 1 m over 12 m of ground. Its angle is tan⁻¹(1 ÷ 12) = 4.76°. Type atan(1÷12).

Logarithms: log vs ln

• log is the base-10 logarithm: log(100) = 2, because 10² = 100.
• ln is the natural logarithm, base e (about 2.718): ln(e) = 1.

Use log for decibels, pH and orders of magnitude; use ln for continuous growth, decay and most calculus.

Example: how many years does money take to double at 8% compound interest? Years = ln(2) ÷ ln(1.08) = 0.693 ÷ 0.077 = 9.0 years. Type ln(2)÷ln(1.08).

Powers and roots

• xʸ raises a number to any power: 2^10 = 1,024.
• x² squares the value: type the number, press x², and the calculator adds ^2.
• √ is the square root: sqrt(144) = 12.
• cbrt is the cube root: cbrt(27) = 3.
• 1/x gives the reciprocal: 1/(8) = 0.125.

For other roots, use a fractional power: the 4th root of 81 is 81^(1÷4) = 3.

Factorials

n! multiplies all whole numbers from 1 to n: 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials count arrangements: 5 books can be arranged on a shelf in 120 ways.

Factorials grow fast. 20! is about 2.4 × 10¹⁸, and beyond 170! the result is too large for the calculator to represent, so it shows Error.

Percentages

The % key turns a number into a fraction of 100, so it works inside longer expressions:

• 50% = 0.5
• 200×15% = 30
• 1500×(1+18%) = 1,770 (adding 18% GST)

For everyday percentage questions such as percentage change, the Percentage Calculator is quicker.

Order of operations

The calculator follows standard order of operations: brackets first, then powers, then multiplication and division, then addition and subtraction. So 2+3×4 = 14, not 20. Use brackets whenever you're unsure: (2+3)×4 = 20.

A common trap is a negative number raised to a power. Write (−3)^2 to get 9. Use the brackets and the − key to build the expression, or press +/- to flip the sign of the number you just typed.

Constants

• π ≈ 3.14159265: circles, waves, rotation. Area of a circle with radius 7 = π × 7² ≈ 153.94.
• e ≈ 2.71828183: growth and decay, compound interest.

Precision

Results are shown to 10 significant digits, which is more than enough for school, engineering estimates and finance. Very small rounding differences (like 0.30000000000000004 in raw computer arithmetic) are tidied up automatically.

Worked problems

Pythagoras. A TV is 120 cm wide and 68 cm tall. What's the diagonal? sqrt(120^2+68^2) = 137.9 cm, about 54 inches.

Combinations. How many ways can you pick 3 people from 10? The formula is 10! ÷ (3! × 7!). Type 10!÷(3!×7!) = 120.

Compound interest. ₹2,00,000 at 7.5% a year for 10 years: 200000×1.075^10 = ₹4,12,206 (rounded).

Height from an angle. You stand 40 m from a building and the angle to the top is 35°. Height = 40 × tan(35) in DEG mode: 40×tan(35) = 28.0 m (plus your eye height).

Half-life. A substance with a 5-year half-life: how much of 80 g remains after 12 years? 80×0.5^(12÷5) = 15.2 g.

Calculator or spreadsheet?

Use the calculator for one-off answers and checking a formula. Use a spreadsheet when you need the same calculation for many rows, want to change inputs and see results update, or need to show your working to someone else.

Quick reference

Button	Does	Example
sin cos tan	Trig ratios	sin(30) = 0.5 (DEG)
sin⁻¹ cos⁻¹ tan⁻¹	Angle from ratio	tan⁻¹(1) = 45 (DEG)
log	Base-10 log	log(1000) = 3
ln	Natural log	ln(e) = 1
xʸ	Power	2^8 = 256
√ / cbrt	Roots	sqrt(81) = 9
n!	Factorial	6! = 720
%	Divide by 100	200×15% = 30

Related tools

• Fraction Calculator for exact fraction answers
• Statistics Calculator for mean, median and standard deviation