Case 1
- Bottom radius
- 5
- Top radius
- 3
- Vertical height
- 4
219.211186
Open with these valuesFrustum Surface Area Calculator
219.211186units²
Result: 219.211186 units²Enter the vertical height, not the slanted side — this one works the slant out for you, as √((R − r)² + h²). The total covers both circular ends plus the curved band between them. For an open bucket, subtract the top circle πr².
The numbers at a glance
Held fixed: Bottom radius 5.000, Top radius 3.000.
| Vertical height | Result |
|---|---|
| 1.000 | 163.012668 |
| 2.000 | 177.900277 |
| 3.000 | 197.431537 |
| 4.000Your value | 219.211186 |
| 5.000 | 242.158104 |
| 6.000 | 265.767562 |
| 7.000 | 289.783268 |
| 8.000 | 314.064044 |
Worked examples
Case 2
- Bottom radius
- 7
- Top radius
- 4
- Vertical height
- 6
436.022409
Open with these valuesCase 3
- Bottom radius
- 10
- Top radius
- 2
- Vertical height
- 8
753.242398
Open with these valuesHow it's calculated
A = π(R + r)·√((R − r)² + h²) + πR² + πr²
- StepMeasure the radius of the wide end and of the narrow end.
- StepMeasure the height straight between the two circles.
- ResultRead the total area in the square of the unit you entered.
Reference table
| Bottom, top, height | Slant | Total area |
|---|---|---|
| 1, 0.5, 2 | 2.061553 | 13.641830 |
| 2, 1, 1 | 1.414214 | 29.036612 |
| 5, 3, 4 | 4.472136 | 219.211186 |
| 7, 4, 6 | 6.708204 | 436.022409 |
| 10, 2, 8 | 11.313708 | 753.242398 |
Questions
How do you find the surface area of a frustum?
Add the two circular ends to the curved band: π(R + r) times the slant height, plus πR² and πr². A frustum with radii 5 and 3 and height 4 comes to about 219.21 square units.
Do I enter the height or the slanted side?
The vertical height. The calculator derives the slant itself from √((R − r)² + h²), which is 4.472136 for radii 5 and 3 with height 4.
What if my bucket has no lid?
Subtract the top circle, πr². For radii 5 and 3 that is π × 9, about 28.27, leaving roughly 190.94 square units of material.
Why is the slant longer than the height?
Because the side leans outward as well as rising. Only when both radii are equal do the two coincide, and the frustum becomes a cylinder.
Sources and last check
Information, not professional advice.