Scientific Calculator

A full scientific calculator with trigonometry, logarithms, powers, roots, factorials, and brackets. Type your expression or use the buttons, and switch between degrees and radians.

How it is calculated

Your expression is broken down into small parts — numbers, symbols, brackets, and function names.

These parts are reordered using a method called the shunting-yard algorithm, so the correct order of operations is followed.

The reordered expression is then solved step by step.

Nothing you type is ever run as computer code — only basic maths is worked out, so it is completely safe.

Formula

Operators: + − × ÷ ^ % !

Functions: sin cos tan asin acos atan log ln sqrt cbrt abs exp

Constants: π, e

Order: Brackets → powers → × ÷ → + −

Worked example

Evaluating an expression with mixed precedence.

Expression: 2 + 3 × 4²

Powers first: 4² = 16

Then multiplication: 3 × 16 = 48

Then addition: 2 + 48 = 50

Answer: 50 (not 400, which is what left-to-right would give)

What is the Scientific Calculator?

The scientific calculator on this page evaluates a full expression that you type or build with buttons. It supports the four operations, powers with ^, factorials with !, brackets, trigonometric functions and their inverses, log to base 10, natural log ln, square and cube roots, absolute value and e raised to a power, with the constants π and e. A switch sets whether angles are in degrees or radians.

It is aimed at Class 9 to 12 students working through trigonometry, logarithms and physics numericals, engineering and science undergraduates, and anyone who needs more than a basic phone calculator. Because the whole expression is read at once, it follows the standard order of operations, and a short history shows your last few results so you can reuse them.

How to calculate it by hand

1. Decide whether your angles are in degrees or radians and set the mode first.

2. Write the expression with explicit operators, using * for multiplication and brackets around every function argument, such as 6*sin(65).

3. Evaluate brackets first, then functions and factorials, then powers from right to left, then multiplication and division from left to right, and finally addition and subtraction.

4. For trigonometry in degree mode, the angle is converted internally using radians = degrees × π ÷ 180.

5. Keep full precision in intermediate steps; round only the final answer.

6. Check the result with a quick estimate, such as knowing sin 65° is a little under 1.

How the expression is read

The calculator does not run your input as computer code. It breaks the text into tokens: numbers, operators, brackets and approved function names. The shunting-yard algorithm then rearranges these into postfix order, where each operator follows its operands, and a stack evaluates them. Precedence decides the order: ^ binds tightest and groups from the right, so 2^3^2 is 2^9 = 512. Multiplication, division and % come next, then + and −. Anything unrecognised is rejected with an error instead of a guess.

Degrees, radians and trigonometry

A full turn is 360 degrees or 2π radians, so one degree is π/180 radians. Computer maths libraries always work in radians, so in degree mode sin, cos and tan convert your angle first, and the inverse functions convert their answer back into degrees. School trigonometry and heights-and-distances questions use degrees. Calculus, physics of oscillations and anything involving arc length use radians. Getting the mode wrong is the most common reason a trigonometric answer looks absurd, such as sin(30) returning −0.988 in radian mode.

Features that behave differently from textbooks

Three details matter here. First, % is the remainder operator, so 7 % 3 = 1; it does not mean percent. Divide by 100 yourself. Second, a leading minus follows the textbook rule and is applied after a power, so -2^2 gives −4. Write (-2)^2 when you mean 4. Third, multiplication must be typed, so 2π gives an error while 2*π works. Displayed answers are rounded to 12 significant figures, which hides tiny floating-point errors such as sin 30° coming out as 0.49999999999999994.

Worked example, step by step

Meera leans a 6 m ladder against a wall so that it makes an angle of 65° with the ground, and wants the height it reaches and the distance of its foot from the wall.

Ladder length: 6 m

Angle with the ground: 65°

Angle mode: Degrees

The ladder is the hypotenuse, so height = 6 × sin 65° and foot distance = 6 × cos 65°.

In degree mode, type 6*sin(65). sin 65° = 0.906307787037, so the height is 5.43784672222 m.

Type 6*cos(65). cos 65° = 0.422618261741, so the foot is 2.53570957044 m from the wall.

Check with Pythagoras: sqrt((6*sin(65))^2+(6*cos(65))^2) returns 6, the ladder length.

Answer: The ladder reaches about 5.44 m up the wall, and its foot is about 2.54 m from the wall.

Common mistakes to avoid

Leaving the calculator in radian mode for a degree question, or the other way round.

Typing 50% expecting 0.5; here % is the remainder operator and the expression is incomplete.

Writing -3^2 and expecting −9; this calculator gives 9, so use -(3^2).

Omitting the * in expressions like 2π or 3(4+5), which returns an error.

Using log when the formula needs ln, or the other way round.

Expecting a number for tan(90) in degree mode; tan 90° is undefined, and the calculator reports it as undefined.

Where it is used

Heights and distances questions in Class 10 trigonometry.

Physics numericals involving sin, cos, powers of ten and square roots.

Chemistry calculations with logarithms, such as pH = −log[H⁺].

Counting problems with factorials, such as 5!/(2!*3!) for combinations.

Engineering and finance formulas that combine powers, roots and e.

Frequently asked questions

Why does 2 + 3 × 4 give 14 rather than 20?

Multiplication is always done before addition. If you want to add first, use brackets: (2 + 3) × 4 = 20.

What is the difference between log and ln?

log uses base 10, so log(1000) = 3. ln is the natural log, which uses base e, and is used in growth and interest formulas.

Should I use degrees or radians?

Use degrees for everyday geometry and most schoolwork. Use radians for calculus and advanced maths. The mode buttons let you switch, and this setting applies to all trigonometry functions.

Is it safe to type anything into it?

Yes. Your input is read as maths, not as computer code, so only basic calculations happen. Anything it does not understand is simply shown as an error.

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