🪣 Right Cylinder Calculator: find A, V, A_l, A_b
Calculate all properties of a right circular cylinder
How to Use This Calculator
Enter Radius and Height
Input the radius of the circular base and the height of the cylinder. Make sure both values are positive numbers.
Click Calculate
Press the "Calculate All Properties" button to compute the total surface area (A), volume (V), lateral area (A_l), and base area (A_b).
Review All Results
View all calculated properties: total surface area (all surfaces), volume (space inside), lateral area (curved surface only), and base area (one circular base).
Formulas
Base Area: A_b = πr²
Area of one circular base
Lateral Area: A_l = 2Ï€rh
Area of the curved surface (side)
Total Surface Area: A = A_l + 2A_b = 2πrh + 2πr² = 2πr(h + r)
Sum of lateral area and both bases
Volume: V = πr²h
Base area × height
Where:
- r = radius of the circular base
- h = height of the cylinder
- A = total surface area
- V = volume
- A_l = lateral (curved) surface area
- A_b = area of one circular base
- π ≈ 3.14159
Example 1: Cylinder with radius 5 units, height 10 units
Base Area = π × 5² = 25π ≈ 78.54 units²
Lateral Area = 2 × π × 5 × 10 = 100π ≈ 314.16 units²
Total Surface Area = 100π + 2(25π) = 150π ≈ 471.24 units²
Volume = π × 5² × 10 = 250π ≈ 785.40 units³
Example 2: Cylinder with radius 3 units, height 8 units
Base Area = π × 3² = 9π ≈ 28.27 units²
Lateral Area = 2 × π × 3 × 8 = 48π ≈ 150.80 units²
Total Surface Area = 48π + 2(9π) = 66π ≈ 207.35 units²
Volume = π × 3² × 8 = 72π ≈ 226.19 units³
About Right Cylinder Calculator
A right circular cylinder is a 3D shape with two parallel, identical circular bases connected by a curved surface. This calculator finds all key properties: total surface area (A), volume (V), lateral area (A_l - the curved side), and base area (A_b - one circular base) from just the radius and height.
When to Use This Calculator
- Engineering: Calculate volumes and surface areas for cylindrical tanks, pipes, or containers
- Architecture: Design cylindrical columns, pillars, or structures
- Manufacturing: Determine material requirements for cylindrical products
- Mathematics Education: Teach students about 3D geometry and cylinder properties
- Construction: Estimate materials (paint, metal, concrete) for cylindrical structures
- Packaging: Calculate capacity and surface area for cylindrical containers
Why Use Our Calculator?
- ✅ Complete Properties: Calculates A, V, A_l, and A_b all at once
- ✅ Instant Results: Get all measurements immediately from just radius and height
- ✅ Step-by-Step Display: See formulas and calculations for each property
- ✅ 100% Accurate: Uses precise mathematical formulas
- ✅ Educational: Helps understand cylinder geometry relationships
- ✅ Completely Free: No registration required
Understanding Right Circular Cylinders
A right circular cylinder consists of:
- Two Circular Bases: Parallel, identical circles with radius r, each with area πr²
- Curved Surface: A rectangle wrapped around the bases with area 2Ï€rh
- Height (h): Perpendicular distance between the two bases
- Radius (r): Radius of the circular bases
- Volume: Space inside = πr²h (base area × height)
- Lateral Area: Area of the curved surface only = 2Ï€rh
- Base Area: Area of one circular base = πr²
- Total Surface Area: Lateral area + both bases = 2πrh + 2πr² = 2πr(h + r)
Real-World Applications
Storage Tanks: A cylindrical water tank has radius 2 m and height 5 m. Volume = π × 4 × 5 ≈ 62.83 m³ (capacity). Total surface area ≈ 87.96 m² (paint/material needed). Lateral area ≈ 62.83 m² (curved surface only).
Pipes: A pipe with radius 0.5 m and height 10 m has volume ≈ 7.85 m³ (material volume) and lateral area ≈ 31.42 m² (outer surface area for coating).
Columns: A cylindrical column with radius 0.3 m and height 3 m has base area ≈ 0.28 m² (one end) and total surface area ≈ 6.21 m² (all surfaces for finishing).
Frequently Asked Questions
What is a right circular cylinder?
A right circular cylinder is a 3D shape with two parallel, identical circular bases connected by a curved surface that is perpendicular to the bases. "Right" means the bases are directly aligned (not slanted), and "circular" means the bases are circles.
What's the difference between lateral area and total surface area?
Lateral area (A_l) includes only the curved surface (2πrh). Total surface area (A) includes the curved surface plus both circular bases (2πrh + 2πr²). If you're wrapping only the sides, use lateral area. If including the ends, use total surface area.
How is cylinder volume related to base area?
Cylinder volume equals base area times height: V = (πr²) × h = πr²h. This is similar to the volume of a prism: volume = base area × height. The base area is πr², and multiplying by height gives the full volume.
Can I calculate if I only know the diameter?
Yes! If you have the diameter (d), the radius is half: r = d/2. Then use the radius in all formulas. For example, if diameter = 10, then radius = 5.
How is this different from a cone?
A cylinder has parallel circular bases of equal size. A cone has one circular base and tapers to a point. A cone's volume is (1/3) of a cylinder with the same base and height. A cylinder's lateral area is 2πrh, while a cone's is πrs (where s is slant height).
What if the cylinder is open at one end?
If open at one end, total surface area = lateral area + one base = 2πrh + πr² = πr(2h + r). Volume remains the same (πr²h) since it's the space inside regardless of whether ends are open.