A scientific calculator can look intimidating, with its rows of buttons labelled sin, cos, log, ln and xy. In reality, you only need to understand a handful of ideas to use it confidently for school, university, engineering or everyday problems. This guide explains each group of functions with simple examples you can try on our free online Scientific Calculator.
1. The order of operations
Calculators do not simply work from left to right. They follow the standard order of operations, often remembered as PEMDAS or BODMAS:
- Parentheses (brackets) first.
- Exponents and roots next.
- Multiplication and division, from left to right.
- Addition and subtraction, from left to right.
That is why 3 + 4 × 2 = 11, because the multiplication happens first, while (3 + 4) × 2 = 14. When you are unsure how an expression will be read, add parentheses. This is especially important with division: an expression such as 8 ÷ 2(2 + 2) is read differently by different calculators, and some give 16 while others give 1. Writing 8 ÷ (2 × (2 + 2)) or (8 ÷ 2) × (2 + 2) removes any doubt.
2. Degrees and radians
Angles can be measured in two units. In degrees, a full turn is 360°. In radians, a full turn is 2π (about 6.283). Trigonometric functions give different answers depending on the mode:
- In degree mode, sin(30) = 0.5.
- In radian mode, sin(30) is about −0.988, because 30 is read as 30 radians.
To get the same 0.5 in radian mode, enter sin(π/6), since π/6 radians equals 30 degrees. If a trigonometry answer looks unexpected, the angle mode is the first thing to check. Use degrees for most school geometry and radians for calculus and physics.
3. Sine, cosine and tangent
In a right-angled triangle, these functions relate an angle to the sides:
- sin = opposite ÷ hypotenuse
- cos = adjacent ÷ hypotenuse
- tan = opposite ÷ adjacent
Useful values to remember in degrees: sin(30°) = 0.5, cos(60°) = 0.5 and tan(45°) = 1. The inverse functions sin⁻¹, cos⁻¹ and tan⁻¹ (also written arcsin, arccos, arctan) work backwards: they take a ratio and return the angle. For example, sin⁻¹(0.5) = 30° in degree mode. Note that tan(90°) is undefined, so a good calculator shows an error instead of a huge number.
4. Logarithms
A logarithm answers the question: "what power do I need?" Two types appear on every scientific calculator:
- log is the base-10 logarithm. Since 10³ = 1000, log(1000) = 3.
- ln is the natural logarithm, with base e ≈ 2.71828. Since e¹ = e, ln(e) = 1, and ln(10) is about 2.3026.
Logarithms are used for earthquake and sound scales, pH in chemistry, compound growth and decay, and many formulas in science and finance. You cannot take the logarithm of zero or a negative number, and the calculator will report an error.
5. Powers, roots and factorials
- x² and xʸ: 2^10 = 1024, and 5² = 25. Negative exponents give fractions: 2^−2 = 0.25.
- Square root √ and cube root ∛: √144 = 12 and ∛27 = 3. The square root of a negative number is not a real number, so you will see an error.
- Factorial n!: the product of all whole numbers from 1 to n. 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials grow extremely fast, and 170! is the largest value most calculators can handle.
6. Constants and percentages
The button π inserts 3.14159…, the ratio of a circle's circumference to its diameter, and e inserts Euler's number. For a circle with radius 5, the area is π × 5², which is about 78.54. The % function divides by 100, so 50% becomes 0.5 and 200 × 15% equals 30.
Common mistakes to avoid
- Forgetting to switch between degrees and radians.
- Leaving a parenthesis open, or placing it in the wrong spot.
- Confusing the minus sign for subtraction with the negative sign: −2² is −4, but (−2)² is 4.
- Mixing up log and ln.
- Rounding too early. Keep full precision during the calculation and round only the final answer.
Practice with the online calculator
Open our Scientific Calculator and try the examples above. You can type the whole expression using your keyboard, use the on-screen buttons on a phone, reuse the last result with ANS and review your last five calculations in the history. Everything runs in your browser, so nothing you enter is uploaded or stored.