Scientific Calculator
Evaluate square roots, trig functions, logarithms, exponentials, powers, reciprocals, and absolute values with full workings.
Scientific Calculator — input your values
What does this math calculator do?
The scientific calculator evaluates the functions you would find on a scientific handheld: square roots, sine, cosine, and tangent, natural and common logarithms, exponentials, squares, cubes, reciprocals, and absolute values. For trigonometric functions you can choose degrees or radians.
Unlike a simple numeric calculator, every result comes with the mathematical identity that defines the operation — for example, √16 = 16^(1/2) = 4 — so you can see the reasoning behind each answer and use it to learn the material.
Formula and variables
Logarithms require x > 0, the square root requires x ≥ 0, the reciprocal requires x ≠ 0, and tangent is undefined at odd multiples of 90° (or π/2).
| Symbol | Meaning |
|---|---|
| x | The input value |
| θ | Angle in degrees or radians |
| e | Euler's number, approximately 2.71828 |
Worked example
Find the square root of 81 and the sine of 30 degrees.
- √81 = 81^(1/2) = 9 because 9 × 9 = 81.
- 30° in radians is 30 × π/180 = π/6 ≈ 0.5236.
- sin(π/6) = 0.5.
Answer: √81 = 9 and sin(30°) = 0.5.
Tips and common mistakes
Tips
- On this calculator, trig functions accept either degrees or radians — for exam work, check which mode your problem expects.
- Memorize the common trig values: sin 0 = 0, sin 30° = 1/2, sin 45° ≈ 0.707, sin 60° ≈ 0.866, sin 90° = 1.
- Use log₁₀ when working with powers of ten: log₁₀(1000) = 3 because 10³ = 1000.
- The square root is a fractional power: √x = x^(1/2), and the cube root is x^(1/3) — this is how fractional exponents work.
Common mistakes to avoid
- Entering trig angles in degrees when your formula expects radians (or the reverse).
- Taking the log of zero or a negative number, which is undefined.
- Treating tan(90°) as a large number instead of recognizing it is undefined.
Scientific Calculator — frequently asked questions
What is the difference between ln and log?
ln is the natural logarithm with base e (about 2.718), while log on this calculator means base 10. They are related by the change of base formula: log₁₀(x) = ln(x) ÷ ln(10).
How do I switch between degrees and radians?
Use the angle mode radio buttons above the input. Degrees divide a full circle into 360 parts; radians divide it into 2π parts, so 180° = π radians.
Why is the square root of a negative number an error?
Because no real number multiplied by itself gives a negative result. The answer would be an imaginary number, which is outside the scope of this real-number calculator.
What does e^x mean?
It is Euler's number (≈ 2.71828) raised to the power of x, also written exp(x). It models continuous growth and appears throughout calculus and finance.
Why is tan(90°) undefined?
Tangent equals sine divided by cosine, and cos(90°) = 0, so tan(90°) = 1/0, which is not defined. The function has a vertical asymptote there.
Can I use this for the functions on a physical scientific calculator?
Yes, this covers the core ones — root, trig, log, exponent, powers, reciprocal, and absolute value — and it shows the working that a physical calculator hides.