Scientific Calculator

How to use: Introduction: How this scientific calculator works

This page provides a lightweight, browser-based scientific calculator for evaluating common math expressions. It supports everyday arithmetic (+, -, *, /), powers (^), square roots (sqrt), logarithms (ln and log), exponentials (exp), and trigonometric functions (sin, cos, tan). You can also insert the constants pi (π) and e (Euler’s number).

The calculator has two displays. The Expression display shows the expression you are building. The Result display shows the most recent computed value. When you press =, the calculator evaluates the expression and updates the result. If evaluation fails, the result will show Error and the note below the detailed result will explain common causes.

Quick start (step-by-step)

1. Choose an Angle mode. Use Degrees for inputs like 30, 45, and 90. Use Radians for inputs like pi/2 and 2*pi.
2. Click buttons to build your expression. Function buttons automatically add an opening parenthesis, for example sin(. You must close it with ) if you include parentheses in your expression (see notes below).
3. Press = to evaluate. Press C to clear the expression and start over.

Limitations and assumptions: Supported functions, formulas, and assumptions

The calculator evaluates expressions using standard mathematical definitions. The keypad supports the following functions and operators. These descriptions are written to match what you see on the buttons, so you can translate a math problem into a valid expression.

• Trigonometry: sin(x), cos(x), tan(x). The meaning of x depends on the selected angle mode.
• Natural logarithm: ln(x) computes the logarithm base e. It is defined for x > 0 in the real numbers.
• Base-10 logarithm: log(x) computes the logarithm base 10. It is also defined for x > 0 in the real numbers.
• Exponential: exp(x) means e^x. For example, exp(1) equals e.
• Powers: a^b raises a to the power b. This is useful for squares (5^2), cubes (2^3), and general exponentiation.
• Square root: sqrt(x) computes √x. For real-number results, use x ≥ 0.
• Constants: pi inserts π (approximately 3.14159) and e inserts Euler’s number (approximately 2.71828).

Angle mode conversion (degrees vs radians)

Trigonometric functions in JavaScript use radians internally. This calculator follows that convention. When you select Degrees, the calculator converts your input to radians before calling the trig function. The conversion is: radians = degrees × π / 180. When you select Radians, the input is used as-is.

Operator precedence and grouping

Expressions are evaluated using typical precedence rules: exponentiation is evaluated before multiplication and division, and multiplication/division are evaluated before addition/subtraction. Parentheses control grouping. For example, 2^3+4 equals 12 because 2^3 is evaluated first, while 2^(3+4) equals 128 because the parentheses force 3+4 to be evaluated first.

Worked examples you can try

These examples are designed to confirm that the calculator is in the correct angle mode and to show common patterns. If your result differs, check the angle mode, check that parentheses are closed, and confirm you did not accidentally insert an extra operator.

1. Degrees example (sine): set Angle mode to Degrees. Enter sin(30) and press =. The expected result is approximately 0.5. This matches the well-known triangle ratio sin(30°) = 1/2.
2. Radians example (cosine): set Angle mode to Radians. Enter cos(pi) and press =. The expected result is approximately -1. This matches the unit circle value cos(π) = −1.
3. Logarithms: enter log(1000) to get 3 because 10³ = 1000. Then try ln(e) to get 1 because ln(e) = 1.
4. Exponentials: enter exp(2) to compute e² (about 7.389056...). This is common in growth/decay models and calculus.
5. Powers and roots: enter 2^10 to get 1024. Then enter sqrt(81) to get 9.
6. Combined expression: in Radians mode, try sin(pi/6)^2 + cos(pi/6)^2. The result should be close to 1, illustrating the identity sin²(x) + cos²(x) = 1.

Common mistakes and troubleshooting

If you see Error, it usually means the expression could not be evaluated. The most common reasons are syntax issues (like missing parentheses) or domain issues (like taking a log of a non-positive number). Use the checklist below to diagnose problems quickly.

• Unclosed parentheses: if you entered sin(30 without a closing ), evaluation will fail. Close each function call: sin(30), log(100), sqrt(9).
• Trailing operators: expressions like 2+ or 5* are incomplete. Add the missing number or remove the trailing operator.
• Domain restrictions: ln(x) and log(x) require x > 0 for real results. sqrt(x) requires x ≥ 0 for real results.
• Angle mode mismatch: if you expect sin(30°) = 0.5 but you are in radians mode, sin(30) will be a different value. Switch to degrees or use radians like sin(pi/6).
• Tangent near asymptotes: tan(x) grows very large near odd multiples of π/2 (or 90°). Large outputs or overflow can occur, especially if you are very close to an asymptote.
• Rounding and display precision: results are shown with practical precision. Very large or very small values may show rounding differences compared with high-precision tools.

Practical notes (what this calculator is best for)

This calculator is ideal for quick checks, studying, and everyday problem solving. For example, you can verify a trigonometry homework step, compute a logarithm while learning about orders of magnitude, or explore how exponentials behave. It is also useful for sanity-checking intermediate steps in longer calculations.

For professional or safety-critical work (engineering tolerances, financial reporting, medical dosing), you should verify results with a dedicated tool and follow the rounding and significant-figure rules required by your context. Different tools may display slightly different rounding depending on precision settings.

Mini FAQ

What does ln mean?

ln is the natural logarithm (log base e). It is commonly used in calculus and exponential growth/decay. Example: ln(e) = 1 and ln(1) = 0.

What does log mean here?

log is base-10 logarithm. Example: log(100) = 2 because 10² = 100.

Why do I need degrees vs radians?

Degrees are common in geometry and many classroom problems, while radians are standard in calculus and most programming libraries. The same angle can be written as 90° or π/2 radians.

Can I type on my keyboard?

Yes. You can click the keypad buttons, and you can also type characters like parentheses on your keyboard. The on-screen keypad is provided for convenience and consistency across devices.