What is factorial (n!) and how is it calculated?

Factorial is the product of a positive integer with every smaller positive integer down to 1: n! = n × (n−1) × … × 2 × 1. For example, 5! = 5×4×3×2×1 = 120. By definition, 0! = 1. Type the number and press n!. Factorial is only defined for 0 and positive integers; permutation (nPr) and combination (nCr) are both built on factorial.

Is this online calculator safe — is my data sent anywhere?

Yes. This scientific calculator runs entirely in your browser (client-side). The expressions and results you enter are never sent to a server — every calculation happens on your device. History is kept only for the current page session. The code also avoids the unsafe eval function; expressions are processed with a dedicated parser (tokenizer + parser). It even works offline once the page has loaded.

Scientific Calculator | Online Trig, Log, Exponents & Factorial

Trigonometry, logarithms, exponents, roots, factorials, and more. Parentheses, keyboard support, degree/radian/grad mode; with memory, calculation history, and a shareable link.

𝑎/𝑏 Fraction: off M: 0

DEC0

BIN0

OCT0

HEX0

🕘 Calculation history

Quick answer A scientific calculator handles sin, cos, tan and inverse trig, ln/log/log2, exponents (^), square root and nth root, factorial (!), permutations/combinations, and parenthesized expressions. Choose an angle mode below, type an expression, and press = — the result is calculated instantly.

3.1415927π (pi) — insert

2.7182818e (Euler) — insert

1.6180340φ (golden ratio) — insert

1.4142136√2 — insert

⚙️ How it works: This tool processes expressions with a safe parser (its own tokenizer + parser); it does not use eval, and no data is ever sent to a server. Results are computed with IEEE-754 double-precision floating point; very large/small numbers and some decimals may round in the last digit. For trigonometry, make sure the DEGREE / RADIAN / GRAD mode above is set correctly. Function keys open a parenthesis automatically; an unclosed parenthesis is completed automatically when you press =.

🧮 Scientific Calculator — ToolPico ↗

What is a scientific calculator, and how do you use one?

How trigonometry, logarithms, exponents, roots, and factorials actually work, and how to use them step by step with this tool.

A scientific calculator goes beyond the four basic operations to compute trigonometric functions (sin, cos, tan), logarithms (ln, log, log2), exponents and roots, factorials, permutations/combinations, and complex parenthesized expressions. The calculator on this page runs entirely in your browser: type the expression using the keypad or your keyboard, set operation precedence with parentheses, and press = to get the result.

How do you calculate sin, cos, and tan?

Quick answerFirst choose the angle mode. In degree mode, sin(30) = 0.5; in radian mode, sin(π/6) = 0.5. For the inverse operation, the sin⁻¹ (asin), cos⁻¹ (acos), and tan⁻¹ (atan) keys convert a ratio back into an angle: in degree mode, asin(0.5) = 30.

2nd key — unlocks the inverse/secondary function of the trig, hyperbolic, and log keys (sin ↔ sin⁻¹, ln ↔ eˣ, √ ↔ ∛).
Angle mode — DEGREE, RADIAN, or GRAD. A full circle is 360° = 2π radians = 400 grad.
Hyperbolic — sinh, cosh, tanh and their inverses (asinh, acosh, atanh) are independent of the angle mode.

Exponents, square roots, and nth roots

Quick answerUse ^ for exponents: 2^10 = 1024. There are dedicated x² / x³ keys for squares and cubes. Square root is √(16) = 4, cube root is ∛(27) = 3. For a root of any degree, the ⁿ√ key inserts root(n, x): root(4, 81) = 3 (the 4th root of 81).

Logarithms: the difference between log, ln, and log2

Quick answerlog is base 10 (log(1000) = 3), ln is the natural logarithm with base e (ln(e) = 1), and log2 is base 2 (log2(8) = 3). For any other base, type logn(base, number): logn(3, 81) = 4.

Factorial, permutations, and combinations

Quick answerFactorial: 5! = 120, and by definition 0! = 1. Permutation (ordered): nPr(5,2) = 20. Combination (unordered): nCr(5,2) = 10. All three are only defined for 0 and positive integers.

Common calculations

One-click expressions loaded straight into the calculator. Each one has a shareable link.

Reference tables

Citable, evergreen values: a basic trigonometry angle table, exponents/roots/factorials, logarithms, and angle unit conversions.

sin, cos, and tan values for common angles (degrees)
Angle	sin	cos	tan
0°	0	1	0
30°	0.5	0.8660	0.5774
45°	0.7071	0.7071	1
60°	0.8660	0.5	1.7321
90°	1	0	undefined
180°	0	−1	0
270°	−1	0	undefined
360°	0	1	0

tan 90° and tan 270° are undefined (cos = 0). Due to floating point, the calculator may display these as a very large number.

Squares, cubes, square roots, and factorials for 1–10
n	n²	n³	√n	n!
1	1	1	1	1
2	4	8	1.4142	2
3	9	27	1.7321	6
4	16	64	2	24
5	25	125	2.2361	120
6	36	216	2.4495	720
7	49	343	2.6458	5,040
8	64	512	2.8284	40,320
9	81	729	3	362,880
10	100	1000	3.1623	3,628,800

Base-10 (log), natural (ln), and base-2 (log2) logarithms of selected numbers
x	log x	ln x	log2 x
1	0	0	0
2	0.3010	0.6931	1
e ≈ 2.7183	0.4343	1	1.4427
5	0.6990	1.6094	2.3219
10	1	2.3026	3.3219
100	2	4.6052	6.6439
1000	3	6.9078	9.9658

Angle unit conversions: degree · radian · grad
Degree	Radian	Grad
0°	0	0
30°	π/6 ≈ 0.5236	33.33
45°	π/4 ≈ 0.7854	50
60°	π/3 ≈ 1.0472	66.67
90°	π/2 ≈ 1.5708	100
180°	π ≈ 3.1416	200
360°	2π ≈ 6.2832	400

Conversion: radian = degree × π/180 · grad = degree × 10/9. In this tool, simply select the mode above to get the correct calculation.

Add this calculator to your site (embed code)

Embed the scientific calculator on your own website for free. Copy the code below into your HTML — the tool runs in a simplified view and links back to this page as its source.

Embed (iframe) code

The embedded tool has a fixed layout; you can adjust the height value to fit your site. No ads or personal data, runs entirely client-side.

Math terms glossary

Short definitions of the core concepts used in this calculator.

Trigonometric functionsin, cos, and tan link an angle to a ratio. Their inverses asin, acos, atan convert a ratio back into an angle.

RadianAn angle measured in terms of the radius. A full circle is 2π radians. radian = degree × π/180.

GradAn angle unit that divides a full circle into 400 units. 90° = 100 grad.

Factorial (n!)The product of n and every positive integer below it: 5! = 120. 0! is defined as 1.

Logarithm (log)Finds what power a given base must be raised to, to produce a number. log(1000)=3 because 10³=1000.

Natural logarithm (ln)A logarithm with base e ≈ 2.71828. ln(e)=1. Used in growth and decay problems.

Exponent (^)Repeated multiplication of a base by itself. 2^10 = 1024. Exponentiation is right-associative: 2^3^2 = 2^9.

RootThe inverse of exponentiation. √ is square root, ∛ is cube root; root(n,x) is the nth root of x.

Permutation (nPr)An ordered selection of r items from n: n!/(n−r)!. nPr(5,2)=20.

Combination (nCr)An unordered selection of r items from n: n!/(r!(n−r)!). nCr(5,2)=10.

Scientific notationWriting a very large or small number as a×10ⁿ. The EXP key inserts ×10^.

AnsThe last calculated result. The Ans key lets you reuse the previous answer in a new calculation.

Short guides

Practical answers to the most common usage questions.

How do you convert between radians and degrees?

To convert degrees to radians, multiply by π/180: 90° × π/180 = π/2 ≈ 1.5708. To convert radians to degrees, multiply by 180/π. The practical shortcut in this tool: just switch the angle mode above — the same expression gives a different result depending on the selected unit.

For example, if you want the sine of an angle given in degrees, choose DEGREE mode; for calculus problems, RADIAN mode is usually used. Grad is used in surveying and some engineering fields (a full circle is 400 grad).

What does the 2nd (second function) key do?

The 2nd key activates the secondary/inverse function of the function keys. While pressed, sin → sin⁻¹, cos → cos⁻¹, tan → tan⁻¹, ln → eˣ, log → 10ˣ, log2 → 2ˣ, √ → ∛, and the hyperbolic keys switch to their inverses (asinh, acosh, atanh).

Inverse trigonometry is used to find an angle from a ratio: if you know the opposite/hypotenuse ratio in a triangle, asin gives you the angle. The result's unit follows the selected angle mode — degree, radian, or grad.

How do you calculate combinations, like lottery odds?

When order doesn't matter, use combination (nCr). For example, in a 6-number draw from 49 numbers, the total number of possible tickets is nCr(49,6) = 13,983,816. The odds of a single ticket hitting the jackpot are the inverse of that number.

When order does matter (like 1st, 2nd, 3rd place), use permutation (nPr): the number of ways to rank the top 3 finishers out of 10 people is nPr(10,3) = 720. Both keys expect an n value, a comma, and an r value.

Frequently asked questions

How do you use a scientific calculator?

First choose the angle mode (degree, radian, or grad) if you'll use trigonometry. Type the expression using the keypad or your keyboard; function keys open a parenthesis automatically (sin(), exponent uses ^, factorial uses !. Set precedence with parentheses and press =. The result is shown large, added to the history, and can be reused in the next calculation with Ans.

How do you calculate sin, cos, and tan?

They are the trigonometric ratios of an angle. In degree mode, sin(30) = 0.5; in radian mode, sin(π/6) = 0.5. For the inverse, the sin⁻¹, cos⁻¹, tan⁻¹ (asin, acos, atan) keys convert a ratio into an angle; in degree mode, asin(0.5) = 30.

What is factorial (n!)?

The product of a positive integer with every positive integer below it, down to 1: n! = n × (n−1) × … × 1. For example, 5! = 120, and by definition 0! = 1. Type the number and press n!. Only defined for 0 and positive integers.

What is the difference between radians and degrees?

Degrees divide a full circle into 360; radians divide it into 2π. Conversion: radian = degree × π/180. So 180° = π radians, 90° = π/2 radians. Grad divides a full circle into 400 (90° = 100 grad). Choose the correct mode for the result to come out right.

What's the difference between log and ln?

log is base 10: log(1000) = 3. ln is the natural logarithm, base e ≈ 2.71828: ln(e) = 1. There's also a log2 (base-2) key: log2(8) = 3. For a different base, use logn(base, number).

Is this online calculator safe?

Yes. This tool runs entirely in your browser (client-side); your expressions are never sent to a server. The code does not use eval; expressions are processed with a dedicated parser. History is kept only for the current session and clears when you close the page.

How do you calculate permutations (nPr) and combinations (nCr)?

Permutation is ordered: nPr = n!/(n−r)!. Combination is unordered: nCr = n!/(r!(n−r)!). Press the key and type n, a comma, then r — e.g. nPr(5,2): nPr(5,2)=20, nCr(5,2)=10. Example: nCr(49,6) = 13,983,816.

How do you enter scientific notation (exponential numbers)?

The EXP key adds ×10^ to the expression. For 6.022×10²³, type 6.022, press EXP, then type 23. For a negative exponent, use ×10^-9. If a result is very large or small, the tool also returns it automatically in scientific notation.

How do you convert numbers between decimal, binary, octal, and hexadecimal?

Switch to BASE-N mode above the keypad, then pick the base you're typing in from the DEC / BIN / OCT / HEX tabs. The tool shows the same value converted into all four bases at once, and the AND, OR, XOR, NOT, and bit-shift (<<, >>) keys run bitwise operations directly — e.g. 1010 AND 0110 = 0010 in binary.

Can this calculator show a result as a fraction?

Yes. Turn on the 𝑎/𝑏 Fraction toggle above the keypad, and any result with a clean fractional equivalent is shown as a reduced fraction next to the decimal value — e.g. 0.75 = 3⁄4 or 0.3333… ≈ 1⁄3. It's off by default since not every decimal has a short exact fraction.

Methodology & accuracy

ToolPico's Scientific Calculator is a free, independent tool. The calculation engine processes expressions with a safe tokenizer and a recursive-descent parser; standard mathematical operator precedence is applied: parentheses & functions → factorial/percent → unary minus → exponent (right-associative) → multiplication/division/mod → addition/subtraction. Trigonometric functions operate in the selected angle mode (degree/radian/grad); hyperbolic functions are independent of the mode.

Limitations: Results are produced with JavaScript's double-precision (IEEE-754) arithmetic, giving roughly 15 significant digits of precision; undefined values such as tan(90°) may appear as a very large number. Factorial overflows above 170 (Infinity). The tool is evergreen: it does not rely on any externally updated data. Last updated: July 19, 2026. Results are for informational purposes only.

Scientific Calculator

What is a scientific calculator, and how do you use one?

How do you calculate sin, cos, and tan?

Exponents, square roots, and nth roots

Logarithms: the difference between log, ln, and log2

Factorial, permutations, and combinations

Common calculations

Reference tables

Add this calculator to your site (embed code)

Math terms glossary

Short guides

Frequently asked questions

Methodology & accuracy

🔗 Add this tool to your site