Scientific Calculator
A free scientific calculator with sin, cos, tan, logs, roots, powers, factorials and degree/radian modes. Type or tap; the answer updates as you type.
Type directly with your keyboard — Enter evaluates, Esc clears. Works with *, /, ^, sqrt(), pi, and 6.02E23 notation (capital E; a lowercase e is Euler’s number).
What Scientific Calculator Does
This scientific calculator evaluates full expressions (trigonometry, logarithms, roots, powers, factorials and percentages) with a live answer that updates as you type. You can click the keys like a handheld calculator or type straight into the box, and every result is kept in a history list you can click to reuse.
Under the keys is a real expression parser with written-down rules rather than a call to JavaScript’s eval. That matters because calculators genuinely disagree on some expressions. The rules this one follows are listed in full below, so when your textbook, phone and this page give different answers you can see exactly why.
In degree mode, the standard angles return exact values: sin(180) is 0 and cos(90) is 0, rather than the 1.22 × 10⁻¹⁶ that raw floating-point arithmetic produces, and tan(90) is reported as undefined instead of as an enormous number.
How to Use Scientific Calculator
- Choose DEG or RAD for trigonometric functions
- Type an expression or build it with the buttons; the answer preview updates live
- Press = or Enter to store the result as Ans
- Click any line in History to reuse that expression
How Scientific Calculator Works
How an expression is evaluated
tokenize → parse by precedence, highest first: postfix ! and % → power ^ (right to left) → unary minus → × ÷ and implied multiplication (left to right) → + − → result rounded to 12 significant digits for display
- implied multiplication
- 2π, 3(4) and (1+2)(3+4) multiply, at the same level as × and ÷. So 6÷2(1+2) is (6÷2)×3 = 9, the convention most software calculators use.
- right-associative power
- 2^3^2 = 2^9 = 512, and −3^2 = −9, as in written math.
- degree mode
- Exact results at the angles people type: sin(180) is 0, not 1.2 × 10^-16, and tan(90) is reported as undefined.
- 12 digits
- Display rounding hides binary floating-point noise, so 0.1+0.2 shows 0.3 rather than 0.30000000000000004.
Worked example
6÷2(1+2), then 2^3^2, then sin(30) in DEG mode
- (1+2) = 3; 6÷2 = 3; 3 × 3 = 9
- 3^2 = 9 first (right to left), then 2^9 = 512
- sin(30°) = 0.5, exactly
Result: 9, 512 and 0.5. Values of 10^15 or more, or smaller than 10^-9, switch to scientific notation.
Order of Operations Used
Highest priority first. Operators on the same row are applied left to right unless noted.
| Priority | Operation | Example | Result |
|---|---|---|---|
| 1 | Parentheses and function calls | 2 × (3 + 4) | 14 |
| 2 | Factorial !, percent % | 5! ÷ 4 | 30 |
| 3 | Powers ^ (right to left) | 2^3^2 | 512 |
| 4 | Negation − | −3^2 | −9 |
| 5 | Multiply ×, divide ÷, implied multiplication | 6 ÷ 2(1 + 2) | 9 |
| 6 | Add +, subtract − | 10 − 4 + 1 | 7 |
Exact Trig Values in Degree Mode
Returned exactly for these angles (and their equivalents every 360°).
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 0.5 | 0.866025403784 | 0.57735026919 |
| 45° | 0.707106781187 | 0.707106781187 | 1 |
| 60° | 0.866025403784 | 0.5 | 1.73205080757 |
| 90° | 1 | 0 | undefined |
| 180° | 0 | −1 | 0 |
How to Read Your Result
Why −3² is −9 and not 9
In written math, −3² means “the negative of three squared”. The minus sign is applied after the power, so the answer is −9. If you mean the square of negative three, write (−3)^2, which gives 9. Some phone calculators apply the minus sign first; this one follows the written convention.
The 6 ÷ 2(1 + 2) argument
Implied multiplication — a number written directly against a parenthesis — is treated here exactly like ×, so the expression is worked left to right as (6 ÷ 2) × 3 = 9. A different convention, still found in some textbooks and on older handhelds, gives implied multiplication higher priority and returns 1. Neither is a calculator bug; the expression is ambiguous, and extra parentheses remove the doubt.
Why results are shown to 12 significant digits
Numbers are stored as IEEE 754 double-precision binary floating point, which cannot represent most decimals exactly. Rounding the displayed answer to 12 significant digits hides that storage noise — 0.1 + 0.2 displays as 0.3 — while still showing far more precision than any practical measurement has.
Limitations & Accuracy Notes
- Calculations use double-precision floating point: about 15–17 significant digits. Results beyond ±1.8 × 10³⁰⁸ overflow, and factorials stop at 170!.
- It evaluates numbers rather than symbols, so it cannot simplify algebra, solve for x or give exact fractions and surds.
- Negative numbers raised to fractional powers, such as (−8)^(1/3), are reported as not real rather than returning the real cube root. Use ∛(−8) for that.
- Statistics, complex numbers, base conversion and graphing are not included; use a dedicated tool for those.
Frequently Asked Questions
Should I use DEG or RAD mode?
Use DEG when your angles are in degrees — geometry, surveying and most school trigonometry problems. Use RAD for calculus, physics formulas with ω or θ in radians, and anything involving π inside the trig function. The same key gives very different answers: sin(30) is 0.5 in DEG mode but −0.988 in RAD mode.
What order of operations does this calculator follow?
Parentheses first, then factorial and percent, then powers (right to left, so 2^3^2 is 2^9 = 512), then negation, then multiplication and division left to right, then addition and subtraction. Negation sits below powers, so −3^2 is −9, matching how the expression is written on paper.
What is the answer to 6 ÷ 2(1 + 2)?
This calculator gives 9, because it treats the implied multiplication in 2(1+2) the same as ×, working left to right: 6 ÷ 2 = 3, then 3 × 3 = 9. Some textbooks and older handheld calculators give implied multiplication higher priority and return 1. The expression is genuinely ambiguous, so write 6 ÷ (2(1+2)) or (6 ÷ 2)(1+2) to say what you mean.
Why does 0.1 + 0.2 show 0.3 here but 0.30000000000000004 elsewhere?
Computers store most decimals as binary fractions, and 0.1 has no exact binary form, so the true stored sum is fractionally off. This calculator rounds results to 12 significant digits, which hides that storage noise while keeping far more precision than any printed answer needs.
How do I enter scientific notation like 6.02 × 10²³?
Use the EXP key or type a capital E: 6.02E23. A lowercase e is always Euler’s number (2.71828…), so 2e means 2 × e.
How does the % key work?
x% divides x by 100, so 50% is 0.5 and 200 × 15% is 30. Handheld calculators disagree about expressions like 50 + 10% (some give 55, some 50.1); this calculator always gives 50.1. To add 10% to 50, type 50 × 1.1 or 50 + 50 × 10%.
What is the largest factorial it can calculate?
170! (about 7.26 × 10³⁰⁶). 171! exceeds the largest number a standard double-precision float can hold, so it shows as overflow. Factorials are only defined here for whole numbers of zero or more.
Can I type instead of clicking the buttons?
Yes. Click into the expression box and type: * and / work for × and ÷, ^ for powers, and names like sqrt(), ln(), log(), pi and Ans. Enter evaluates, Esc clears, and the answer preview updates as you type.
References & Further Reading
- Goldberg, “What Every Computer Scientist Should Know About Floating-Point Arithmetic” (ACM Computing Surveys, 1991) — Why decimal results carry tiny binary errors