Everyday volume of a parallelepiped problems come down to one relationship between edge length ab (a), ∠dae (α), edge length ad (b), ∠bae (β), edge length ae (c), ∠bad (γ), px, pγ, pz, qx, qγ, qz, rx, rγ, rz, sx, sγ, sz, one way, cos and sin. This calculator turns those numbers into temp variable(square of scalar triple product)v squared, surface area of the parallelepiped and volume of the parallelepiped, with the working shown so you can check the result rather than simply trust it.
What Is the Volume of a Parallelepiped Calculator?
The volume of a parallelepiped calculator works through edge length ab (a), ∠dae (α), edge length ad (b), ∠bae (β), edge length ae (c), ∠bad (γ), px, pγ, pz, qx, qγ, qz, rx, rγ, rz, sx, sγ, sz, one way, cos and sin to give you temp variable(square of scalar triple product)v squared, surface area of the parallelepiped and volume of the parallelepiped.
It is aimed at the case where you know the method but not the arithmetic: schoolwork, a quick check on a worked example, or a figure that needs to be right first time.
How the Volume of a Parallelepiped Works
Each step is applied in order and depends only on the values before it, which makes it possible to follow the calculation rather than take it on trust.
If you are working through the same problem by hand afterwards, compare the intermediate values. That is where a mistake usually shows itself.
Checking Your Own Working
Round sensibly as you go and keep the full precision in the calculator. Rounding too early is the most common way of getting a right method to give a wrong answer.
Where a result should be a whole number, such as a count, check it against the constraint that produced it. A fraction of a person is a sign that something upstream needs revisiting.
A Worked Example
Working through an example, with edge length ab (a) set to 10, ∠dae (α) set to 5, edge length ad (b) set to 2, the calculator returns a1 of 3, and a2 of -98, and a3 of 90. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out temp variable(square of scalar triple product)v squared?
Enter edge length ab (a), ∠dae (α), edge length ad (b), ∠bae (β), edge length ae (c), ∠bad (γ), px, pγ, pz, qx, qγ, qz, rx, rγ, rz, sx, sγ, sz, one way, cos and sin. The calculator then works through the relationship and reports temp variable(square of scalar triple product)v squared, surface area of the parallelepiped and volume of the parallelepiped.
What does the volume of a parallelepiped actually calculate?
It takes edge length ab (a), ∠dae (α), edge length ad (b), ∠bae (β), edge length ae (c), ∠bad (γ), px, pγ, pz, qx, qγ, qz, rx, rγ, rz, sx, sγ, sz, one way, cos and sin and converts them into temp variable(square of scalar triple product)v squared, surface area of the parallelepiped and volume of the parallelepiped using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter edge length ab (a)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Does anything you type get stored?
No. The whole calculation runs inside your browser, and nothing you enter is uploaded, logged or sent anywhere.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.