Cylinder net
A cylinder net is the flat pattern that folds into a cylinder: one rectangle and two circles. The rectangle is 2πr wide (the circumference of the base) and h tall; the circles have radius r and sit on its top and bottom edges. For r = 1 in and h = 4 in, the net of a cylinder is a 6.28 in × 4 in rectangle plus two circles 2 in across.
Contents
Rectangle: 2πr × h. Two circles of radius r. With r = 1 in and h = 4 in: rectangle 6.28 in × 4 in, circles 2 in across, paper area 2πr(r + h) = 31.42 in².
The calculator above draws the net for any radius or diameter and height, gives the size of each piece and prints it at true size when you work in inches, centimeters or millimeters. The rest of this page explains how to draw one by hand, how to make it stand up, and how the net leads to the surface area formula.
The three pieces of a net for a cylinder
| Piece | Dimensions | Area | r = 3 in, h = 8 in |
|---|---|---|---|
| Rectangle (curved side) | 2πr × h | 2πrh | 18.85 in × 8 in = 150.80 in² |
| Top circle | radius r | πr² | 28.27 in² |
| Bottom circle | radius r | πr² | 28.27 in² |
| Whole net | 2πr² + 2πrh | 207.35 in² |
The rectangle's width is the one number students get wrong. It is not the diameter and not the radius: it is the distance around the circle, 2πr ≈ 6.28 × r. Roll the rectangle up and that edge has to meet itself after going exactly once around the end circle.
How to draw a cylinder net by hand
- Choose r and hDecide the radius and the height of the finished cylinder, in the same unit.
- Work out the circumferenceMultiply the radius by 2π. For r = 2.5 cm, 2π × 2.5 = 15.71 cm.
- Draw the rectangleDraw it 15.71 cm long and as tall as the cylinder, say 10 cm.
- Add the circlesSet a compass to the radius, 2.5 cm. Draw one circle touching the top edge of the rectangle and one touching the bottom edge. They can touch anywhere along those edges.
- Add glue tabsDraw a narrow strip along one short side of the rectangle, and small notched tabs around each circle or along the long edges.
- Cut, fold, glueCut around the outline, roll the rectangle into a tube with the tab inside, then glue the circles to the ends.
That metric example takes a sheet about 15.71 cm wide and 10 + 4 × 2.5 = 20 cm tall, before tabs: it fits on an A4 sheet (21 × 29.7 cm). The imperial version from the top of the page, r = 1 in and h = 4 in, needs 6.28 in × 8 in and fits on a US letter sheet.
How big a cylinder fits on one sheet?
The rectangle is the limiting piece. On a letter sheet turned sideways, the 11 in edge allows a circumference up to 11 in, so a radius up to 11 ÷ 2π ≈ 1.75 in, and the height plus both circles (h + 4r) must stay under 8.5 in. On A4 turned sideways, the 29.7 cm edge allows a radius up to about 4.73 cm. Leave room for margins and tabs, or print the circles on a second sheet. For larger models, split the rectangle into two halves, each πr wide, and join them with a second tab.
Glue tabs: making the net hold
A net without tabs has nothing to glue. Add a strip along one short edge of the rectangle; it slides under the opposite edge when you roll the tube. For the ends, two methods work:
- Tabs on the circles. Draw small trapezoids around each circle, fold them up, and glue them inside the tube.
- Tabs on the tube. Draw a row of narrow triangles along both long edges of the rectangle, fold them inward, and glue the circles on top of them.
Score the folds with a dull point and a ruler before folding. Thin card holds its round shape better than plain paper. The tabs add paper but not surface: when you compute the area, count only the rectangle and the circles.
From the net to the surface area formula
A net shows the whole outside of the solid laid flat, so its area is the surface area. Add the pieces: two circles, 2 × πr², and the rectangle, 2πr × h:
A = 2πr² + 2πrh = 2πr(r + h)
For r = 1 in and h = 4 in, that is 2π × 1 × 5 = 31.42 in² of paper. For r = 2.5 cm and h = 10 cm, 2π × 2.5 × 12.5 = 196.35 cm². This is exactly how the surface area of a cylinder formula is built. The rectangle alone is the lateral surface area, 2πrh: the size of a can label.
The net also explains why the curved face counts as a face even though it is not flat: it is one piece. The faces, edges and vertices of a cylinder page covers that count: 3 faces, 2 edges, 0 vertices.
Variants: open cylinder, half cylinder, angled cut
Open cylinder or tube
Leave out one circle for a cup or an open box; leave out both for a tube. The tube's net is just the rectangle.
Net of a half cylinder
A half cylinder, such as a trough, has four pieces: the curved side unrolled into a rectangle πr wide and h tall, the flat face as a rectangle 2r × h, and two half-circles of radius r. For r = 3 in and h = 8 in: 9.42 in × 8 in (75.40 in²), 6 in × 8 in (48 in²) and two half-circles totaling 28.27 in². The whole net is 151.67 in². Its volume is on the half cylinder volume page.
Tube cut at an angle
If one end of a tube is cut at an angle θ from square, the unrolled edge is no longer straight: it becomes a wave. Measured from the middle of the cut, its height at a distance x along the rectangle is r × tan θ × sin(x ÷ r). For θ = 45° and r = 1 in, the edge rises and falls 1 in either side of the midline over one full wave of 6.28 in. Wrapped around a pipe, a paper template of that wave gives a clean line for an angled cut. The slice it produces is an ellipse; its area is on the cross-sectional area of a cylinder page.
Common mistakes with the net of a cylinder
- Rectangle as wide as the diameter. A 2 in diameter needs a 6.28 in rectangle, not 2 in.
- Circles drawn with the diameter as radius. The circles come out twice too wide and will not fit the tube.
- Both circles on the same edge. Put one on the top edge and one on the bottom edge, or the net folds into a tube with two lids at one end.
- Counting tabs in the area. They are construction aids, not part of the surface.
Check before cutting: wrap a strip of paper around the circle you drew. Its length should match the rectangle's width.
Net electric flux through a cylinder
In physics, "net flux through a cylinder" is a different idea: the total electric flux through the closed surface, counted outward. By Gauss's law it equals the enclosed charge divided by ε₀, Φ = q ÷ ε₀. With no charge inside, the net flux is zero. In a uniform field parallel to the axis, the flux entering one end (−E × πr²) cancels the flux leaving the other (+E × πr²), and none crosses the curved side. With a long line charge λ along the axis, all the flux crosses the curved side, of area 2πrh, so E × 2πrh = λh ÷ ε₀ and E = λ ÷ (2πε₀r). The same three surfaces as in the net, two circles and one curved face, do the work.
To go from the shape to what it holds, the cylinder volume calculator uses the same radius and height to give V = πr²h.
FAQ
What does the net of a cylinder look like?
A rectangle with a circle attached to its top edge and another to its bottom edge. The rectangle is the curved side unrolled; the circles are the two ends. The rectangle's width equals the circumference of the circles, 2πr.
How many faces does a cylinder net have?
Three pieces: two circles and one rectangle. They match the three faces of a closed cylinder: two flat circular faces and one curved face.
How long should the rectangle be in a cylinder net?
Exactly the circumference of the end circles: 2πr, or π × diameter. For circles of radius 1 in, the rectangle is 6.28 in long. If it is shorter, the tube will not close around the circles.
How do you find the surface area from the net?
Add the areas of the pieces: two circles, 2 × πr², plus the rectangle, 2πr × h. That gives the surface area formula of a cylinder, 2πr² + 2πrh.
What is the net of a half cylinder?
A curved rectangle πr wide and h tall, a flat rectangle 2r wide and h tall, and two half-circles of radius r. For r = 3 in and h = 8 in the pieces total about 151.67 in².
Related
- Surface area of a cylinderThe surface area of a cylinder is A = 2πr² + 2πrh. Get the total, lateral and base areas from a radius or diameter, with worked examples in inches and cm.
- Lateral areaThe lateral area of a cylinder is L = 2πrh, the curved side only. Calculator, why the formula works, and examples with can labels and painted poles.
- Faces, edges, verticesA cylinder has 3 faces (2 flat, 1 curved), 2 curved edges and 0 vertices. See why some textbooks disagree and how it compares with cones and prisms.
Updated October 12, 2026