मुफ़्त वैज्ञानिक कैलकुलेटर
त्रिकोणमितीय फ़ंक्शन, लॉगरिदम, मेमोरी और बहुत कुछ के साथ पूर्ण-विशेषताओं वाला वैज्ञानिक कैलकुलेटर।
यह कैसे काम करता है
उन्नत गणितीय संक्रियाओं के लिए इस वैज्ञानिक कैलकुलेटर का उपयोग करें। त्रिकोणमितीय फ़ंक्शन के लिए डिग्री और रेडियन के बीच स्विच करें।
विशेषताएँ
- त्रिकोणमितीय फ़ंक्शन · डिग्री या रेडियन में sin, cos, tan, asin, acos, atan
- उन्नत गणित · लघुगणक (log, ln), फैक्टोरियल, वर्गमूल, घात, स्थिरांक (π, e)
- मेमोरी फ़ंक्शन · मान संग्रहीत और पुनः प्राप्त करने के लिए M+, M−, MR, MC
अक्सर पूछे जाने वाले प्रश्न
डिग्री और रेडियन में क्या अंतर है?
डिग्री और रेडियन कोण मापने के दो तरीके हैं। अधिकांश लोग डिग्री (360° = पूरा चक्कर) का उपयोग करते हैं। गणित/भौतिकी के लिए रेडियन का उपयोग करें।
मेमोरी फ़ंक्शन का उपयोग कैसे करें?
M+ वर्तमान परिणाम को मेमोरी में जोड़ता है, M− घटाता है, MR सहेजे गए मान को याद करता है और MC मेमोरी साफ़ करता है।
क्या मेरा डेटा सहेजा जाता है?
नहीं। सभी गणनाएँ पूरी तरह आपके ब्राउज़र में होती हैं। कुछ भी संग्रहीत नहीं किया जाता या सर्वर पर नहीं भेजा जाता।
A short history of the pocket scientific calculator
Before 1972, every working engineer, scientist, navigator, surveyor and pharmacist carried a slide rule. William Oughtred (an English Anglican clergyman and amateur mathematician) invented the linear slide rule around 1622, building on John Napier's 1614 publication of logarithms. It worked by physically aligning logarithmically-scaled wooden, ivory or plastic strips so that addition of distances corresponded to multiplication of underlying values. By the mid-20th century the slide rule was the universal symbol of engineering competence: the Apollo astronauts carried Pickett N600-ES rules to the Moon as backup computation devices, and Buzz Aldrin reportedly used one en route to the lunar surface in 1969. A typical engineer's rule offered 3 to 4 significant digits, accurate enough for most engineering work where input tolerances were already ±5%, but not for the iterative computations postwar science increasingly demanded.
Hewlett-Packard introduced the HP-35 on 1 February 1972 at $395 (roughly $2,800 in 2026 dollars). It was the world's first handheld scientific calculator: shirt-pocket sized, battery-powered, with a 10-digit LED display. Bill Hewlett had personally specified that it must fit in his shirt pocket; the engineering team measured his pocket and used those dimensions as a hard constraint. The "35" referred to the number of keys. It performed all four arithmetic operations, sin/cos/tan and inverses, natural and common logarithms, exponentials, powers, square root, and π. HP's market research projected 10,000 unit sales per year. They sold 100,000 in the first year and over 300,000 by the time the model was retired in 1975.
The slide rule died fast. Within roughly 24 months of the HP-35's release, sales collapsed. K&E, the largest US manufacturer, ceased slide-rule production in 1976 after dominating the industry for 109 years. Texas Instruments responded with the TI-30 in 1976 at $24.95 (a tenth of the HP-35's launch price) and sold approximately 15 million units, making it the device that brought scientific computation into every American high school. Today the TI-84 family dominates US classrooms; the Casio fx-991 series (over 100 million units sold) is the international standard, the exam-permitted device in the UK, India, much of Europe, Australia and most of Asia.
Algebraic vs RPN, a brief detour
There are two main ways to enter a calculation. Algebraic input matches the way an expression is written: 2 + 3 × 4 typed left to right yields 14 (with proper PEMDAS precedence). Reverse Polish Notation (RPN) reverses the relationship: operands are entered first and pushed onto a stack, the operator comes last and consumes the top items. The same calculation in RPN is 2 [ENTER] 3 [ENTER] 4 × +.
RPN was developed by Polish logician Jan Łukasiewicz in 1924 ("Polish notation"); the postfix variant became standard in compiler design as a way to evaluate expressions without parentheses or precedence rules. HP adopted it for the HP-35 and the long-lived HP-12C (introduced 1981, still sold today as one of the longest-lived consumer electronics products in history). RPN avoids parentheses entirely and shows intermediate results on the stack at every step, but it requires a learning curve. Algebraic notation matches what students learn in school and scales cleanly to modern "natural display" calculators. This calculator uses algebraic notation with explicit parentheses keys, the right choice for a browser-based homework tool.
Order of operations and the famous viral problem
The conventional order taught in most of the English-speaking world is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction); the UK and Commonwealth typically use BODMAS (Brackets, Orders, Division and Multiplication…); some regions teach BIDMAS or GEMDAS. All three encode the same hierarchy: parentheses first, then exponents (right-to-left, so 2^3^2 = 2^9 = 512), then multiplication and division at the same precedence level evaluated left-to-right, then addition and subtraction at the same precedence level evaluated left-to-right.
The pair "Multiplication and Division" sits at one precedence level, it is not multiplication-then-division. 8 ÷ 4 × 2 evaluates as (8 ÷ 4) × 2 = 4, not 8 ÷ (4 × 2) = 1. PEMDAS is a memory aid, not an algorithm.
In 2019 a Twitter post asking "what does 8÷2(2+2) equal?" went viral, with users splitting roughly 50-50 between answers of 16 and 1. The disagreement isn't about whether PEMDAS is right; it's about whether implicit multiplication (juxtaposition like "2(2+2)") binds tighter than explicit ÷ at the same precedence level. Strict PEMDAS gives 16; the implicit-multiplication-first convention used in many physics and engineering journals gives 1. The American Mathematical Society and most academic style guides recommend never writing such an expression, always use parentheses to make precedence explicit. This calculator exposes ( and ) keys precisely so you can be unambiguous.
Trigonometric functions, the radian/degree footgun
The single most common source of "the calculator is wrong" complaints is mode mismatch, entering an angle in degrees while the calculator is in radians, or vice versa. sin(90) in degree mode is 1.000; in radian mode it's 0.894. The mode toggle at the top of this calculator is exactly there to prevent that, and the active mode is shown in the display.
Useful exact values worth remembering:
| Angle (deg) | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | undefined |
A full circle is 360° = 2π radians; converting between them is radians = degrees × π / 180. A radian is the angle subtended at the centre of a circle by an arc whose length equals the circle's radius, a definition so natural for calculus that mathematicians prefer it, even though everyday usage favours degrees.
Logarithms, exponentials and constants
Two log functions are conventional: log (base 10, the "common" log) and ln (base e, the "natural" log). Both are inverses of exponentiation: log(1000) = 3 because 10³ = 1000; ln(e²) = 2. Other bases are computed via the change-of-base identity: log_b(x) = ln(x) / ln(b).
Two constants are universally available: π ≈ 3.14159 (the ratio of a circle's circumference to its diameter) and e ≈ 2.71828 (the base of the natural logarithm, equal to the limit of (1 + 1/n)ⁿ as n → ∞). Both are irrational and transcendental.
The IEEE 754 floating-point honesty
All modern scientific calculators (including this one) use IEEE 754 double-precision floating-point arithmetic. Doubles store roughly 15–17 significant decimal digits, which is more than enough for everyday use but produces some surprises:
- 0.1 + 0.2 = 0.30000000000000004: the canonical example. Decimal 0.1 has no exact binary representation (it's a repeating binary fraction, like 1/3 in decimal), so the addition picks up a tiny rounding artefact. Most calculators round the display to hide it, but the underlying value is genuinely off in the 17th digit.
- Factorials cap out fast.
170!is about 7.26×10³⁰⁶, near the largest finite double.171!overflows to infinity. Big factorials need arbitrary-precision libraries. - Trig at extreme angles loses precision.
sin(10²⁰ × π)should be 0 but isn't, because by then most of the angle's bits are lost to floating-point representation error.
For 99% of homework, engineering and finance, IEEE 754 doubles are perfectly fine. For research-grade computation in physics, cryptography or computer algebra, dedicated arbitrary-precision libraries (Python's decimal, GMP, mpmath, or symbolic systems like SymPy and Mathematica) are the right tools.
When you'd reach for a scientific calculator
- Engineering and physics homework: the original target user, still the dominant use case.
- Quick statistics: converting raw numbers to means, basic standard-deviation work, percentile lookups (this tool covers basic arithmetic; for full statistics, a dedicated stats tool is more appropriate).
- Financial back-of-envelope: compound interest with the
x^ykey, ROI percentages, mortgage estimates. - Chemistry: equilibrium constants (logarithms), pH (negative log of hydrogen ion concentration), Avogadro arithmetic.
- Cooking and recipe scaling: fractions, percentages, unit conversions.
- Trigonometry-heavy DIY: calculating diagonal cuts, angles for shelving, roof pitches.
- Currency / unit conversion estimates: multiplication and division to a known rate.
- Verifying spreadsheet output: quick sanity check on a complex formula by re-doing one cell by hand.
More questions
Why is sin(180°) not exactly 0 on most calculators?
Because π itself can't be stored exactly in binary floating-point, the value is a finite approximation, so sin(π) picks up a tiny non-zero residual (typically around 10⁻¹⁶). Most calculators round the display so you see "0," but the underlying value is the floating-point neighbourhood of zero. For symbolic-exact mathematics, a computer algebra system like SymPy, Mathematica or Maple is the right tool.
What's the difference between log and ln?
log is base 10 ("common logarithm"), used in chemistry pH, decibels, the Richter scale, and any context where you're working with powers of 10. ln is base e ≈ 2.71828 ("natural logarithm"), used in calculus, exponential growth/decay, finance (continuously compounded interest), and most physical-science formulas. They're related: log(x) = ln(x) / ln(10) ≈ ln(x) × 0.4343.
Why do my factorials stop working after 170!?
Because IEEE 754 double-precision floating-point can't represent numbers larger than about 1.8 × 10³⁰⁸. 170! ≈ 7.26 × 10³⁰⁶ is just under that limit; 171! ≈ 1.24 × 10³⁰⁹ overflows to infinity. For larger factorials use Python's arbitrary-precision integers (math.factorial(500) works fine) or a symbolic algebra system.
Is the calculator's keyboard input handled?
Most modern web calculators support typing numbers and the basic + − × ÷ operators directly from your keyboard, plus Enter for equals and Backspace to delete. For the scientific functions (sin, log, sqrt, etc.) you'll need to click the on-screen buttons.
Does anything get sent to a server?
No. Every operation runs in your browser using JavaScript's built-in Math object, the same arithmetic engine that powers Node.js, every web app, and every browser-based game. Nothing about your calculations leaves the page; the tool works offline once it's loaded.