Scientific Calculator
A real expression engine — PEMDAS with right-associative powers, implicit multiplication, factorials, and degree or radian trig — evaluated entirely in your browser.
Scientific Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Single-variable arithmetic — no solver, no variables.
- Factorial capped at 170 (the double-precision ceiling).
- tan at a pole returns a huge finite value, not an error.
In short: 3+4*2/(1-5)^2^3 = 3.0001220703125: the (1−5) makes −4, the right-associative power tower gives (−4)^(2^3) = 65,536, and 8 divided by that is 0.0001220703125. Alongside it: 2^3^2 = 512 (not 64), −3^2 = −9, 8/2(2+2) = 16, sin(30°) = 0.5, sqrt(2) = 1.4142135623731, 5! = 120.
Formula
PEMDAS: ( ) → ^ → × ÷ (left to right) → + − (left to right)
2^3^2 = 2^(3^2) = 512 — powers read top-down
−3^2 = −(3^2) = −9 — the sign sits outside the power
8/2(2+2) = 16 — juxtaposition is ordinary ×
[('512', '2^3^2 — right-associative, never 64'), ('−9', '−3^2 — unary minus binds looser'), ('16', '8/2(2+2) — the viral case, settled'), ('170!', 'the factorial ceiling of a double')]
Worked Example
- Type the whole expression — parentheses nest freely.
- Pick degrees or radians for the trig functions.
- Read the result; the convention card explains the order.
- Use the worked-example chips for the famous traps.
- Errors name themselves — nothing is faked.
3+4*2/(1-5)^2^3 = 3.0001220703125; 2^3^2 = 512; −3^2 = −9; 8/2(2+2) = 16; sin(30) in degrees = 0.5; 5! = 120; log(1000) = 3.
Strengths & Limits Of This Model
Where this engine is strong
- Convention-honest: right-assoc powers, −3^2 = −9
- Errors are named, never faked as infinity
- Worked-example chips for the famous traps
Where it stops
- No variables or graphing
- No hyperbolic functions
Practical Use Cases
Homework checks
The full expression, one shot.
Nested powers
Right-associativity done right.
Trig in degrees
The consumer default, honest.
Factorials
Combinatorics warm-ups.
The viral traps
8/2(2+2), settled by convention.
Methodology & Editorial Standards
A recursive-descent parser (expression → term → power → postfix → atom) tokenizes the input, enforces the PEMDAS tiers, evaluates powers right-to-left, binds unary minus looser than ^, treats juxtaposition as ordinary multiplication at term level, and supports the trig/inverse-trig/root/log family plus π, e and factorials (capped at 170). Division by zero, non-real domains and non-finite results are refused with named errors. Display shows the exact double when its literal is short, otherwise 12 significant digits; the exponential card always shows toExponential(6).
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Scientific Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
What is the order of operations this calculator follows?
PEMDAS: parentheses first, then exponents, then multiplication and division together from left to right, then addition and subtraction together from left to right. Equal-precedence operators never outrank each other — 15/3*4 = 20.
Why is 2^3^2 equal to 512 here?
Exponentiation is right-associative: 2^3^2 means 2^(3^2) = 2^9 = 512. Computing (2^3)^2 = 64 reads the tower bottom-up, against the mathematical convention.
What does -3^2 equal?
−9. The power binds tighter than the leading minus, so −3^2 is −(3^2). To square a negative number, parenthesize it: (−3)^2 = 9.
What is 8 divided by 2(2+2)?
16. Parentheses first make 4; then the line is evaluated left to right with the juxtaposition as ordinary multiplication: 8÷2×4 = 16. Implicit multiplication does not get special priority — the strict scientific-calculator convention.
Which functions and constants can I type?
sin, cos, tan, asin, acos, atan, sqrt, abs, ln, log (base 10) and exp; the constants pi (or π) and e; and the postfix factorial, 5! = 120. Juxtaposition multiplies: 2pi works.
Does sin take degrees or radians?
Degrees by default — sin(30) = 0.5. Switch the angle term to 0 for radians and sin(π/6) reads 0.5 the same way.
Does 2pi work without a times sign?
Yes — juxtaposition multiplies: 2pi, 3(4+5), (1+1)(2+2). It counts as ordinary multiplication in the same left-to-right line, which is exactly why 8/2(2+2) resolves to 16.
What happens if I divide by zero?
The page refuses and says so. A result of infinity is a typo wearing a costume — the same discipline applies to square roots of negatives and logs of non-positives.