Scientific Calculator

About Scientific Calculator

What Functions Does This Calculator Support?

This calculator covers the standard scientific function set found on a Casio fx-991EX or Texas Instruments TI-30X IIS - the two models most US and UK exam boards authorise for GCSE, A-level, SAT, and most first-year university courses. The full function set is summarised below.

Category	Functions	Examples
Arithmetic	+ , - , x , / , ( )	(3 + 4) x 2 = 14
Powers	x^y, square root	2^10 = 1024, sqrt(144) = 12
Trigonometry	sin, cos, tan (deg/rad)	sin(30) = 0.5 (degrees mode)
Logarithms	log (base 10), ln (base e)	log(1000) = 3, ln(e) = 1
Factorial	n!	5! = 120, 10! = 3,628,800
Constants	pi (3.14159...), e (2.71828...)	pi x r^2 for circle area

How Does Degrees vs Radians Work?

Degrees divide a full turn into 360 equal parts, while radians measure the same turn as 2π (≈6.2832), the ratio of arc length to radius. The mode you pick only affects the trig functions - everything else behaves identically. NIST defines the radian as the SI coherent unit of plane angle, which is why physics and engineering calculations assume radians by default.

• Degrees mode: sin(90) = 1, cos(60) = 0.5, tan(45) = 1
• Radians mode: sin(pi/2) = 1, cos(pi/3) = 0.5, tan(pi/4) = 1

Everyday use (triangle angles, bearings, slopes, surveying) uses degrees. Radians are required in calculus because the derivative of sin(x) is cos(x) only when x is in radians. One full turn equals 360 degrees or 2π radians, so to convert: radians = degrees x (pi / 180) and degrees = radians x (180 / pi).

What Is the Order of Operations?

The calculator follows the standard precedence rule taught in UK schools as BODMAS and in US schools as PEMDAS. The two acronyms differ only in labels - the underlying rule, codified in the UK National Curriculum (Key Stage 2 and 3) and the US Common Core standards, is identical.

1. Brackets / Parentheses
2. Orders / Exponents (powers, roots)
3. Division and Multiplication (left to right)
4. Addition and Subtraction (left to right)

So 2 + 3 x 4 = 14 (not 20), because multiplication happens before addition. Use parentheses to override: (2 + 3) x 4 = 20. A common exam trap is 6 / 2(1 + 2): modern calculators following strict left-to-right evaluation return 9, because implied multiplication has the same precedence as division. When in doubt, add parentheses.

Worked example: evaluate sqrt(3^2 + 4^2) + log(1000) - 2!. The calculator works through the precedence levels in order: exponents first (3^2 = 9, 4^2 = 16, sum 25), then the sqrt wrapper (sqrt(25) = 5), then log(1000) = 3, then 2! = 2. Final expression: 5 + 3 - 2 = 6. Try it by typing sqrt(3^2 + 4^2) + log(1000) - 2! and pressing =.

How Do the Memory Functions Work?

The memory buttons give you a single scratch register that survives between calculations, mirroring the M+/M-/MR/MC layout on every TI and Casio scientific since the 1980s.

• M+ (Memory Add): Adds the current display value to what is already in memory
• M- (Memory Subtract): Subtracts the current display value from memory
• MR (Memory Recall): Inserts the stored value into your current expression
• MC (Memory Clear): Resets the memory register to zero

Useful for multi-step problems where writing down intermediate results is slower than recalling them. For example, to compute (3 x 7) + (8 x 5): type 3*7, press =, then M+ (memory now holds 21). Type 8*5, press =, then M+ again (memory now holds 61). Press MR to insert 61 into a new expression.

Keyboard Shortcuts

Key	Action
0-9, . (period)	Enter digits
+ - * /	Arithmetic operators
( )	Parentheses for grouping
^	Exponent (e.g. 2^10)
Enter or =	Evaluate expression
Backspace	Delete last character
Escape	Clear all

Useful Formulas Reference

Common formulas this calculator handles in a single expression. Each is verified against textbook values.

Formula	Expression	Example
Circle area	pi x r^2	pi x 5^2 = 78.54
Sphere volume	(4/3) x pi x r^3	(4/3) x pi x 3^3 = 113.10
Pythagorean theorem	sqrt(a^2 + b^2)	sqrt(3^2 + 4^2) = 5
Compound interest	P x (1 + r)^n	1000 x 1.05^10 = 1,628.89
Decibel ratio	10 x log(P1/P2)	10 x log(100) = 20 dB
Exponential decay	N x e^(-kt)	100 x e^(-0.1 x 5) = 60.65
Quadratic formula (one root)	(-b + sqrt(b^2 - 4ac)) / (2a)	a=1, b=-3, c=2 -> 2
Heron's formula (triangle area)	sqrt(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2	3-4-5 triangle: area = 6

For full quadratic solutions including complex roots, use the quadratic calculator. For fractional arithmetic without decimal drift, try the fraction calculator.

What Is the Difference Between log and ln?

log on this calculator is base 10 (common logarithm), while ln is base e ≈ 2.71828 (natural logarithm). They answer different questions. log(x) asks "10 to what power equals x?" - useful for decibels, the Richter scale, pH, and anything measured in orders of magnitude. ln(x) asks "e to what power equals x?" - the natural choice for continuous growth, half-life, and calculus, because the derivative of ln(x) is 1/x.

To convert between them: ln(x) = log(x) x ln(10) ≈ log(x) x 2.3026. Base-2 logarithms (used in information theory and computer science) can be computed with the change-of-base rule: log2(x) = ln(x) / ln(2), e.g. log2(1024) = ln(1024) / ln(2) = 10.

Precision, Limits, and Floating-Point Quirks

This calculator uses JavaScript's 64-bit IEEE 754 double-precision floating-point arithmetic, which gives roughly 15-17 significant decimal digits. That is plenty for exam work, engineering estimates, and everyday maths, but a few limits are worth knowing:

• Factorial cap: results are defined for integers 0-170. 170! is roughly 7.26 x 10^306, which sits just below Number.MAX_VALUE (≈1.798 x 10^308). 171! overflows to Infinity.
• Binary representation error: 0.1 + 0.2 returns 0.30000000000000004. This is not a bug - it reflects the fact that 0.1 cannot be represented exactly in binary, a well-documented property of IEEE 754. The calculator rounds display to 12 significant figures to hide most of this, but edge cases remain.
• tan(90°) and tan(π/2): the true value is undefined, but because π cannot be represented exactly in binary, the calculator returns a very large finite number (≈1.633 x 10^16) rather than Infinity or Error.
• Very large exponents: 2^1024 overflows to Infinity. 10^-324 underflows to 0. These are hard IEEE 754 limits.

For context, the Excel REAL data type and most calculator chips use the same IEEE 754 double, so results here match what you would get in Excel or a TI-84. If you need arbitrary precision (thousands of digits) for cryptography or number theory, use a dedicated symbolic tool - this calculator is optimised for speed and familiarity, not unlimited precision.

Common Mistakes

• Forgetting the mode: sin(30) returns 0.5 in degrees mode and -0.988 in radians mode. Always check the DEG/RAD indicator before a trig calculation.
• Missing the bracket after a function: the calculator inserts the opening bracket automatically when you press sin, cos, tan, log, ln, or sqrt. Make sure you add the closing bracket, or the expression will error.
• Unary minus for negative bases: -2^2 evaluates as -(2^2) = -4 (standard precedence), not (-2)^2 = 4. Wrap negative bases in parentheses: (-2)^2.
• Using log when you meant ln: in scientific literature, "log" sometimes means natural log (especially in pure maths) and sometimes base 10 (especially in engineering and chemistry). On this calculator, log is always base 10.
• Implicit multiplication: 2pi is not recognised - type 2*pi instead. Every multiplication needs an explicit operator.
• Chained percentages: a 20% discount followed by a 10% discount is not a 30% discount. The compound factor is 0.8 x 0.9 = 0.72, so the total reduction is 28%. Build this as price * 0.8 * 0.9.

Which Scientific Calculators Are Exam-Approved?

Exam boards publish approved-calculator lists each year. For UK GCSE and A-level maths, Pearson Edexcel and AQA permit any non-programmable scientific calculator that does not have a QWERTY keyboard, symbolic algebra (CAS), or graphing functions. The Casio fx-83GT CW and fx-85GT CW are the most common classroom models. For Further Maths A-level, graphing calculators like the Casio fx-CG50 are permitted. In the US, the College Board allows the TI-30XS MultiView and TI-36X Pro on the SAT and approves a broader list of graphing calculators for AP Calculus. This web calculator mirrors the non-programmable feature set and is intended for homework and revision, not the exam itself.

For statistical calculations like mean, variance, and standard deviation, use the standard deviation calculator. For plotting functions visually, try the graphing calculator. For quick percentage work, the percentage calculator avoids the typical "percent of" keystroke mistakes.

Sources

• NIST - SI Units (radian as coherent SI unit)
• Wolfram MathWorld - Radian
• Wolfram MathWorld - Order of Operations
• GOV.UK - National Curriculum Mathematics Programmes of Study
• IEEE 754-2019 - Standard for Floating-Point Arithmetic
• MDN - JavaScript Number (IEEE 754 double)
• Britannica - Logarithm