Prisms Similar Ratio Calculator
Calculate dimensions, surface area, and volume ratios between similar prisms with our precise geometry tool
First Prism Dimensions
Second Prism Dimensions
Calculation Options
Similarity Results
Enter dimensions to check if the prisms are similar and see their ratios.
Detailed Calculations
Your prism similarity analysis will appear here.
📐 Common Prism Examples
| Prism Type | Scale Factor (k) | Area Ratio | Volume Ratio |
|---|---|---|---|
| Small Cube | 1 | 1 | 1 |
| Medium Cube | 2 | 4 | 8 |
| Large Cube | 3 | 9 | 27 |
| Small Rectangular | 1 | 1 | 1 |
| Large Rectangular | 1.5 | 2.25 | 3.375 |
| Triangular (small) | 1 | 1 | 1 |
| Triangular (large) | 2 | 4 | 8 |
Note: All examples assume perfect similarity with consistent scaling in all dimensions.
📚 Geometry Tips
Similarity Basics
Two prisms are similar if all corresponding linear dimensions are in the same ratio.
Volume Scaling
Volume scales with the cube of the linear scale factor (k³). Double the dimensions = 8× the volume.
Area Scaling
Surface area scales with the square of the linear scale factor (k²). Triple the dimensions = 9× the surface area.
Proportionality
For perfect similarity, all corresponding angles must be equal and all sides proportional.
Real-world Applications
Used in architecture, model making, and when scaling objects up or down.
Quick Calculations
If you know volume ratio is 8:1, the linear scale factor is 2:1 (since 2³ = 8).
Note: This calculator assumes perfect geometric similarity. For irregular prisms or those with non-uniform scaling, additional calculations may be required.