Cake Filling and Frosting Geometry Calculator
Estimate ideal filling and exterior frosting masses from round-layer geometry and entered densities.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sum between-layer disks, a side annulus over stack height and a top disk over the outer radius.
Filling=(layers−1)πr²f; side=π[(r+s)²−r²]h; top=π(r+s)²t
Worked example
Two 20 cm layers with a single 0.5 cm filling layer contain 50π mL of filling. At 1 g/mL that is about 157.079633 g.
Assumptions and input details
Equal cylindrical layers, constant thickness and entered densities only. Stack height includes filling, side frosting stops below the top disk and corners are not double-counted. Decorative piping, crumb-coat waste, mixing losses, texture and recipe suitability are excluded.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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