Vector Math Calculator (2D & 3D)
Calculate dot and cross products, norms, angles, unit vectors and projections with an interactive 3D direction diagram.
About this vector math calculator (2d & 3d)
Calculate dot and cross products, norms, angles, unit vectors and projections with an interactive 3D direction diagram Computes exact algebraic and numerical metrics directly in your browser using IEEE 754 precision without round-trip latency.
Formula & calculation mechanics
Evaluates high-precision arithmetic, number theory algorithms, and floating-point representations. Arbitrary-precision calculations utilize JavaScript BigInt to compute factorials, combinations ($nCr$), permutations ($nPr$), greatest common divisor (Euclidean algorithm GCD), least common multiple (LCM), and prime factorizations without 64-bit integer overflow. The IEEE 754 visualizer breaks down 32-bit single-precision and 64-bit double-precision floats into Sign (1 bit), Biased Exponent (8/11 bits), and Mantissa/Significand (23/52 bits), modeling denormal numbers, infinities, and NaNs.
Worked numerical calculation
Scenario: What does the example produce?
Sample input:
Processing: Choose 2D or 3D and enter A and B. Calculate, select Deg or Rad and inspect signed projections and unit vectors. Rotate the direction diagram and compare the formulas and numeric results.
Illustrative output:
Domain range & precision boundaries
Enter 2 or 3 comma-separated coordinates, matching the selected dimension. Integers, point decimals, e notation and surrounding whitespace are accepted; no fractions, brackets or thousands separators. Each vector is limited to 256 UTF-16 code units. Inputs are parsed as finite binary64 numbers; underflow may round tiny coordinates or results to zero. Dot and cross products accumulate binary64 products exactly before final rounding. Norms, unit vectors, angles and projections are approximate; values display 12 significant digits. Nonfinite inputs or overflowing results are rejected. Use a common coordinate unit; projection lengths use that unit and dot/cross products its square. No automatic unit conversion. Drag the canvas, use rotation/tilt sliders or focus the diagram and press arrow keys; Home resets to 30°/20°. A is blue, B red, A×B green and the angle arc purple; labels also distinguish arrows. All arrows have unit display length: this shows directions, not relative magnitudes. In 2D vectors lie in z=0; there is no cross-product arrow. Zero vectors have no arrow. Cross direction uses normalized inputs, with a fallback to the raw cross product if normalization loses a tiny component; it may remain visible when the numerical cross magnitude underflows. A view along an arrow can hide it; rotate to inspect. The angle arc is a 24-segment approximation; opposite vectors use one of the possible semicircles. Numeric results provide the accessible equivalent. Runs locally after loading, including offline. No added calculation dependency, external service, fee or usage quota.
Calculations in Vector Math Calculator (2D & 3D) use standard IEEE 754 precision or exact rational models. Verify significant accounting or tax figures with authoritative references.
In-browser calculation boundary
Formula calculations and numeric evaluations in Vector Math Calculator (2D & 3D) run synchronously in the browser JavaScript engine with zero server telemetry.
Mathematical formulas & precision standards
Mathematical constants, IEEE 754 floating-point standards, and numerical analysis specifications:
- NIST Digital Library of Mathematical Functions, §1.2 — Elementary Algebra
- ECMAScript 2026, §6.1.6.1 Number Type
Vector Math Calculator (2D & 3D) verification · Audit standards
How to use it
- Enter, paste, or select your input data into the Vector Math Calculator (2D & 3D) workspace controls.
- Review parameter fields, units, or options configured for Vector Math Calculator (2D & 3D).
- Click the action button or observe immediate live calculations rendered by Vector Math Calculator (2D & 3D).
Frequently asked questions
Which operations are supported by Vector Math Calculator (2D & 3D)?+
Operational requirements for "Which operations are supported by Vector Math Calculator (2D & 3D)?" are verified in local memory during execution of Vector Math Calculator (2D & 3D).
How are zero vectors handled?+
A zero vector has no unit vector. The angle is undefined if either vector is zero; projection onto a zero vector is undefined, while projection of a zero vector onto a nonzero vector is zero. Projection lengths are signed (negative for opposite directions). The angle lies in [0, π] radians or [0, 180] degrees. Cross product is provided only in 3D and follows the right-hand rule.
What are the numerical and display limits?+
Runtime handling of "What are the numerical and display limits?" executes synchronously in your browser tab without remote delays.
What does the example produce?+
Security isolation for "What does the example produce?" ensures zero transmission beyond your local workstation.