About this calculator
Type a calculation the way you would write it, and get the answer to 12 significant figures. The calculator follows the normal order of operations (brackets, powers, multiplication and division, addition and subtraction) and shows the expression back with every bracket written out, so you can check that it was read the way you meant.
Trigonometric functions use degrees or radians as you choose. For focused tools with explanations, see the Logarithm and Trigonometry calculators.
Formula
Order of operations: brackets → factorial ! → powers ^ (evaluated right to left: 2^3^2 = 2^9) → unary minus → × and ÷ (left to right) → + and − (left to right).
−2^2 = −(2²) = −4 2^−1 = 0.5 2π = 2 × π 1/2π = (1/2) × π
A number written directly before a function, constant or bracket is multiplied (2π, 3(4 + 1), 2sin(30)). Implied multiplication has the same priority as ×, so 1/2π means (1/2) × π — write 1/(2π) if you mean the other.
Worked example
2*sin(30) + sqrt(16) / 2^3 in degrees:
- sin(30°) = 0.5, so 2 × 0.5 = 1
- √16 = 4 and 2³ = 8, so 4 ÷ 8 = 0.5
- 1 + 0.5 = 1.5
Other examples: ln(e^2) = 2; 5! = 120; log(1000) = 3; (1.5e3 + 250)*pi/4 = 1374.45.
Assumptions and limitations
- Real numbers only: square roots of negative numbers and other complex results give an error.
- Calculations use IEEE 754 double precision (about 15–16 significant digits). The result is shown to 12 significant figures; “Full precision” shows every stored digit.
- In degrees, sin, cos and tan of exact multiples of 90° are returned exactly (sin 180° = 0, tan 90° undefined).
- The expression is read by a small parser written for this page; it is never run as program code.
References
- IEEE 754-2019 Standard for Floating-Point Arithmetic.
- Conventional order of operations (as in ISO 80000-2 and common calculator practice).