Trig, logarithms, exponents, factorials, permutations, memory, and a running history tape — with full keyboard support. Type or tap; results update live.
A scientific calculator is more than a bigger keypad — it understands the rules of mathematics, from operator precedence to angle modes.
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Walk-through
How to Use This Calculator
4 steps▸
1
Build the expression
Tap the keypad or use your physical keyboard to enter a full expression — for example, 3 + 4 × (2 − 1). Functions like sin, ln, and √ insert an open parenthesis automatically, so you just type the value and close it. The result line evaluates live as you type, and the = key lights up only when the expression is complete and the parentheses balance.
2
Pick the right angle mode
Use the DEG / RAD / GRAD switch before evaluating trigonometry. In DEG, sin(30) = 0.5; in RAD, the same input is interpreted as 30 radians and gives a very different number. The active mode is shown in the badge next to the controls so you always know how angles are read.
3
Use Inv, memory, and Ans
Tap Inv (or 2nd) to flip sin/cos/tan to their inverses and ln/log to eˣ/10ˣ. Store running totals with MS, M+, and M−, and recall them with MR. The Ans key drops your last result into a new expression so you can chain calculations without retyping.
4
Record and reuse from the history tape
Press = to record each calculation on the history tape. Click any past entry to load its expression back into the display for editing, copy the whole tape to your clipboard, or export it as a CSV. History, angle mode, and precision are saved in your browser, so they persist between visits.
The parser respects standard precedence. Exponentiation is right-associative, so 2^3^2 = 2^(3^2) = 512, not (2^3)^2. Unary minus binds looser than exponent, so −2² = −(2²) = −4.
Trig functions convert your input to radians based on the active angle mode before computing, and inverse trig converts the radian answer back to your chosen mode. A full circle is 360°, 2π rad, or 400 grad.
Factorial requires a non-negative integer. Permutations count ordered arrangements; combinations count unordered selections. Both require 0 ≤ r ≤ n with whole numbers.
Logarithm change of base
logᵧ(x) = ln(x) / ln(y)
logᵧ(x, y) computes the logarithm of x to base y using natural logs internally. ln is base e (≈2.71828); log is base 10. Both require a positive argument.
Roots as exponents
ⁿ√x = x^(1/n) · √x = x^(1/2) · ∛x = x^(1/3)
yroot(x, n) raises x to the reciprocal power 1/n. Even roots of negative numbers are not real and return a Math Error; odd roots of negatives are allowed.
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Glossary
Key Terms Explained
6 terms▸
MantissaThe significant-digits part of a number written in scientific notation. In 1.23e+15 the mantissa is 1.23 and the exponent is 15, meaning 1.23 × 10¹⁵.
RadianThe SI unit of angle: the angle subtended by an arc equal in length to the radius. 2π radians = 360°. Most programming languages (and this engine internally) compute trig in radians.
FactorialThe product of all positive integers up to n, written n!. For example 5! = 120. Defined only for non-negative integers; 0! = 1.
Modulo (mod)The remainder after division. mod(a, b) returns a − b·⌊a/b⌋, so mod(17, 5) = 2. Useful for cycles, clock arithmetic, and divisibility tests.
Significant figuresThe digits in a result that carry meaning. The precision selector rounds the displayed answer to this many significant figures (default 10) without changing the stored value used for chaining.
Scientific notationA compact way to write very large or very small numbers as a mantissa times a power of ten, e.g. 6.022e+23. This calculator switches to it automatically beyond about 10¹⁵ or below 10⁻⁹.
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Scenarios
Real-World Examples
3 worked examples▸
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Trig in degrees
sin(30) in DEG mode
Angle mode DEGExpression sin(30)Result 0.5
With the angle mode set to DEG, 30 is read as 30 degrees, and sin(30°) = 0.5. Switch to RAD and the same keystrokes mean sin(30 radians) ≈ −0.988 — a classic source of confusion. Always check the badge before doing trigonometry.
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Combinatorics
Lottery odds with nCr
Expression nCr(49, 6)Result 13,983,816Meaning ways to pick 6 of 49
nCr(49, 6) counts the unordered ways to choose 6 numbers from 49 — about 14 million. That means a single ticket has roughly a 1-in-14-million chance of matching all six. Use nPr instead when order matters, such as ranking finishers in a race.
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Order of operations
Nested expression with exponents
Expression 2 + 3 × 4^2Result 50Why 4² first, then ×3, then +2
The engine evaluates 4² = 16 first (exponents), then 3 × 16 = 48 (multiplication), then 2 + 48 = 50 (addition). Without precedence rules you might wrongly read it left-to-right as ((2+3)×4)² = 400. Add parentheses whenever you want to override the default order.
A scientific calculator is more than a bigger keypad — it understands the rules of mathematics, from operator precedence to angle modes. This guide explains how this tool parses what you type, why trig answers depend on degrees versus radians, when to reach for ln instead of log, and how factorials and permutations actually work.
How expressions are parsed (no eval, ever)
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Rather than executing your input as code, this calculator tokenizes the expression, converts it to Reverse Polish Notation with the shunting-yard algorithm, and evaluates that stack. The practical upshot is correct order of operations every time: exponents before multiplication, multiplication before addition, and right-associative powers so 2^3^2 = 512. Parentheses override the defaults, and the = key stays disabled until your parentheses balance — a built-in guard against the most common typo.
Implicit multiplication is supported, so 2π, 3(4+1), and 2sin(45) all work without an explicit × sign.
Degrees, radians, and gradians
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Trigonometric functions need to know what unit your angle is in. In DEG mode a right angle is 90; in RAD mode it is π/2 ≈ 1.5708; in GRAD mode it is 100. Internally every angle is converted to radians before the sine, cosine, or tangent is computed, and inverse functions convert the radian answer back to your selected mode. If a trig result ever looks wildly wrong, the angle mode is the first thing to check — sin(90) is 1 in degrees but 0.894 in radians.
ln versus log, and the change of base
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ln is the natural logarithm (base e ≈ 2.71828), the inverse of eˣ, and the one that shows up in growth, decay, and calculus. log here is base 10, handy for orders of magnitude, decibels, and pH. For any other base, use logᵧ(value, base) — for example logᵧ(8, 2) = 3. Under the hood it applies the change-of-base identity logᵧ(x) = ln(x)/ln(y).
Factorials, permutations, and combinations
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The factorial key (x!) multiplies every whole number down to 1 and is defined only for non-negative integers, so −3! or 2.5! returns a Math Error. nPr counts ordered arrangements and nCr counts unordered selections; both require whole numbers with 0 ≤ r ≤ n. Because factorials grow explosively, 171! overflows the range of a double-precision number and the calculator reports a Math Error rather than a misleading Infinity.
Memory, Ans, and the history tape
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Five memory keys (MC, MR, M+, M−, MS) let you accumulate a side total while you work, and the M badge lights up whenever memory holds a value. Ans reuses your last result, and pressing an operator right after = automatically chains from the previous answer. Every evaluation is logged to the history tape, which you can click to reuse, copy, or export to CSV — and it persists in your browser between sessions.
Edge cases and error handling
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The calculator returns a clear Math Error instead of a silent wrong answer for division by zero, √ of a negative, ln or log of a non-positive number, asin/acos outside [−1, 1], factorials of negatives or fractions, and overflow. Unbalanced parentheses simply keep the = key disabled until you close them. This fail-loud behavior is deliberate: a calculator that quietly produces NaN or Infinity is worse than one that tells you what went wrong.
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Questions
Frequently Asked Questions
7 questions▸
How do I do exponents and powers?+
Use the xʸ key (or type ^) for any power: 2^10 = 1024. The x² key squares the previous value, and with Inv active it cubes it (x³). For roots, √ gives the square root, ∛ the cube root, and ʸ√x the n-th root via yroot(value, n). Remember that powers are right-associative, so 2^3^2 means 2^(3^2) = 512.
Why does sin(90) give a weird number instead of 1?+
Almost certainly because the calculator is in RAD (radian) mode, where 90 means 90 radians and sin(90) ≈ 0.894. Switch the angle mode to DEG and sin(90) = 1 as expected. The current mode is shown in the badge next to the DEG/RAD/GRAD switch — check it before any trigonometry.
When should I use ln instead of log?+
Use ln (natural log, base e) for continuous growth and decay, compound interest, half-lives, and anything from calculus. Use log (base 10) for orders of magnitude, decibels, the Richter scale, and pH. For any other base, use logᵧ(value, base) — for example logᵧ(1000, 10) = 3.
What is the difference between nPr and nCr?+
Both choose r items from n, but nPr (permutations) counts ordered arrangements while nCr (combinations) counts unordered selections. nPr(5, 2) = 20 ordered pairs; nCr(5, 2) = 10 unordered pairs. Use permutations for things like race finishes and combinations for things like lottery draws or committees.
What does 'Math Error' mean?+
It means the expression is mathematically undefined or out of range — for example dividing by zero, taking √ of a negative number, ln of zero, asin of a value outside [−1, 1], a factorial of a negative or fractional number, or a result too large to represent. Fix the input and the live result returns. Unbalanced parentheses don't error; they just keep the = key disabled until you close them.
How does the history tape work, and is my data saved?+
Every time you press = the calculation is added to the history tape on the right. Click any entry to load its expression back for editing, use Copy to put the whole tape on your clipboard, or CSV to download it. History, your angle mode, and your precision setting are stored locally in your browser only — nothing is uploaded, and there is no signup.
Can I use my physical keyboard?+
Yes. Digits, + − * / ^ ( ) . ! % and comma all map directly; * becomes ×, / becomes ÷, and - becomes minus. Press Enter or = to evaluate, Backspace to delete the last character, Esc to clear, and p to insert π.
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