Surface of Revolution Calculator Calculate the surface area generated by revolving a curve around an axis. Function y = f(x)Parametric Axis of Revolution X-AxisY-Axis Function y = f(x) x(t) y(t) Calculate Surface Area Surface Area In calculus, when a curve is rotated around an axis, it creates a three-dimensional shape called a surface of revolution….
Lemniscate Area Calculator Calculate the area of “Figure-8” shaped curves Bernoullir² = a²cos(2θ) Geronox⁴ = a²(x² − y²) Constant a Calculate TOTAL ENCLOSED AREA A lemniscate is a beautiful, figure‑eight‑shaped curve that often appears in advanced geometry and calculus. One of the most famous examples is the lemniscate of Bernoulli, which looks like a sideways…
Area of Graph Calculator Function f(x) Lower Limit (a) Upper Limit (b) Calculate Area Method Used: Total Area = ∫ |f(x)| dx (Simpson’s Rule Approximation) Graphs are powerful tools that show how one value changes with another. You see graphs in math, physics, economics, engineering, and even daily reports. Sometimes, you don’t just want…
Nonagon Area Calculator Calculate properties of a regular nonagon (9 sides) Side (s) Radius (R) Apothem (a) Side Length (s) Calculate AREA PERIMETER INTERIOR ANGLE 140° RADIUS (R) In geometry, a nonagon is a polygon that has nine sides and nine angles. When all sides and angles are equal, it is called a regular nonagon….
Koch Snowflake Area Calculator Explore the fractal limits of area and perimeter. Inputs Initial Side Length (s) Iterations (n) Max 6 for browser performance. Calculate AREA (n) Limit: PERIMETER (n) Limit: ∞ Math Details Sides: Area Growth: % of Limit The Koch Snowflake is one of the most famous shapes in mathematics. It looks like…
Ring Area Calculator Calculate the area of a circular ring (annulus) using radius or diameter. Radius (R, r)Diameter (D, d) Inputs Outer Radius (R) Inner Radius (r) Outer Diameter (D) Inner Diameter (d) Calculate Ring Area Total Perimeter Thickness (W) In geometry, we often deal with simple shapes like circles, squares, and triangles. But sometimes,…
Donut (Annulus) Area Calculator Calculate the area of a donut-shaped annulus using various input pairs. Calculation Mode Outer Radius & Inner RadiusOuter Diameter & Inner DiameterOuter Radius & Inner DiameterOuter Diameter & Inner RadiusGiven Area & One Dimension Outer Radius (R) Inner Radius (r) Outer Diameter (Dₒ) Inner Diameter (Dᵢ) Outer Radius (R) Inner Diameter…
Overlapping Circles Area Calculator Radius of Circle 1 Radius of Circle 2 Distance Between Centers Select Unit mmcmminft Calculate Overlap Area Formula Used: A = r₁²cos⁻¹((d² + r₁² − r₂²)/(2dr₁)) + r₂²cos⁻¹((d² + r₂² − r₁²)/(2dr₂)) − ½√[(-d+r₁+r₂)(d+r₁−r₂)(d−r₁+r₂)(d+r₁+r₂)] Circles are simple shapes, but when two circles overlap, the shared region between them can become…
Minor Segment Area Calculator Calculate Area of a Circular Segment (Cap) Radius (r) Central Angle (°) Calculate MINOR SEGMENT AREA ARC LENGTH CHORD LENGTH HEIGHT (SAGITTA) Circles are one of the most common shapes in mathematics, engineering, design, and everyday life. From wheels and pipes to pizza slices and water tanks, circles appear everywhere. Sometimes,…
Washer Area Calculator (Annulus Geometry) Choose Input Type Outer/Inner RadiusOuter/Inner Diameter Outer Radius Inner Radius Outer Diameter Inner Diameter Select Unit mmcmminft Calculate Area Formulas Used: Area Outer Circle = π × R² Area Inner Circle = π × r² Washer Area = π × (R² − r²) = Outer − Inner In engineering,…