Contour Volume (Prismoidal) Calculator

Work out contour volume (prismoidal) instantly with clear inputs, formula shown and shareable results.

About Contour Volume (Prismoidal) Calculator

The prismoidal formula, h/3 x (A1 + 4A2 + A3), fits a second order surface through three equally spaced contour areas and is exact for a prismoid. Average end areas treats each pair as a wedge and always over-estimates where the shape is convex, so the difference between the two is the prismoidal correction.

Formulas

Prismoidal formula

V = h/3 x (A1 + 4 A2 + A3), for two equal intervals h

Average end areas

V = h x [(A1 + A2)/2 + (A2 + A3)/2]

Worked example

With the default values below, Contour Volume (Prismoidal) Calculator returns Volume by the prismoidal formula of 2,983.33. Change any input above and every figure here is recalculated in your browser.

Inputs used

Area of the lower contourminimum 0 m²: 1,200 m²
Area of the middle contourminimum 0 m²: 1,500 m²
Area of the upper contourminimum 0 m²: 1,750 m²
Contour intervalminimum 0.01 m: 1 m

Results

Volume by the prismoidal formula: 2,983.33 m³
Volume by average end areas: 2,975.00 m³
Prismoidal correction: -8.33 m³
Total height covered: 2.00 m

Step by step

1Values used
2Prismoidal formula
3Average end areas
4Volume by the prismoidal formula= 2,983.33 m³
5Volume by average end areas= 2,975.00 m³
6Prismoidal correction= -8.33 m³
7Total height covered= 2.00 m

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Contour Volume (Prismoidal) figure worked out?

V = h/3 x (A1 + 4 A2 + A3), for two equal intervals h. The prismoidal formula, h/3 x (A1 + 4A2 + A3), fits a second order surface through three equally spaced contour areas and is exact for a prismoid.

When does the difference matter?

On steep or rapidly changing ground and on large volumes, where the correction can exceed two percent. For flat sites with close contours the two methods agree closely.

What values do I need to enter?

This calculator takes 4 inputs: Area of the lower contour, Area of the middle contour, Area of the upper contour, Contour interval. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.