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表面积计算器
Instant formulas, live results, and step-by-step breakdowns for every 3D shape.
Choose by shape
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Each calculator shows the formula, intermediate values, units, and references so results are easy to check.
球体表面积计算器
SA = 4πr²立方体表面积计算器
SA = 6a²圆柱表面积计算器
SA = 2πr(r + h)圆锥表面积计算器
SA = πr(r + √(r² + h²))长方体表面积计算器
SA = 2lw + 2lh + 2wh三棱柱表面积计算器
SA = PL + 2B棱锥表面积计算器
SA = base + lateral faces椭球体表面积计算器
SA ≈ 4π[((a^1.6b^1.6 + a^1.6c^1.6 + b^1.6c^1.6) / 3)]^(1/1.6)胶囊体表面积计算器
SA = 4πr² + 2πrh圆环面表面积计算器
SA = 4π²Rr圆台表面积计算器
SA = π(R² + r²) + π(R + r)√((R - r)² + h²)球冠表面积计算器
SA = 2πRh + πr²Formula-first calculators
Every result includes the exact formula, substituted values, and a readable step-by-step calculation.
Unit-aware results
Switch between metric and imperial units without leaving the page, including square-unit conversion guidance.
Built for learning
Labelled diagrams, examples, references, and related calculators help users understand the geometry.
Surface area basics
Calculate surface area with confidence
Surface area measures the total exposed area on the outside of a three-dimensional shape. Students use it to check geometry homework, teachers use it to explain nets and formulas, and builders use it to estimate paint, wrapping, insulation, coating, or material coverage. A sphere uses a radius-only formula, a cylinder combines two circular bases with one curved side, and prisms add the areas of matching faces. More specialized shapes, such as ellipsoids, torus forms, capsules, and conical frustums, need formulas that are easy to misread when copied from a textbook. This site keeps the calculator, diagram, formula, and worked steps together so the result is fast but still auditable.
Choose a calculator above, enter positive dimensions, and compare the result with the formula breakdown. For adjacent topics, use the related-shape links on each calculator page or read the articles on derivations, paint coverage, and unit conversion.
FAQ
Surface area questions
What is surface area?
Surface area is the total outside area of a three-dimensional object. It is measured in square units such as m², cm², ft², or in².
How do these calculators work?
Each calculator applies a published geometry formula, substitutes your dimensions, and shows the intermediate steps so the result can be checked by hand.
Can I use different units?
Yes. Choose meters, centimeters, millimeters, feet, inches, or kilometers. Results are shown in the matching square unit.
Are calculations stored?
No. Calculations run in your browser and are not saved as personal history.
Which calculator should I choose?
Choose the page that matches the shape. If the object is a combination of shapes, calculate each part and add the areas that are exposed.
Learn more
文章
为什么球体表面积是 4πr²
Calculate and visualize surface area for common 3-D shapes with clear formulas, examples, and citations.
从展开图理解圆锥和圆台面积
Calculate and visualize surface area for common 3-D shapes with clear formulas, examples, and citations.
用表面积估算涂料用量
Calculate and visualize surface area for common 3-D shapes with clear formulas, examples, and citations.