Whether you are estimating on the spot or checking a result somebody else gave you, the dot product calculator is the quickest way to get from angle between vectors (α), x, x, y, y, z, z and cos to magnitude |a|, magnitude |b| and dot product.
What Is the Dot Product Calculator?
The dot product calculator works through angle between vectors (α), x, x, y, y, z, z and cos to give you magnitude |a|, magnitude |b| and dot product.
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 Dot Product 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 angle between vectors (α) set to 10, x set to 5, x set to 2, the calculator returns dot product of 1,020, and magnitude |a| of 100.24969, and magnitude |b| of 10.3923. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out magnitude |a|?
Enter angle between vectors (α), x, x, y, y, z, z and cos. The calculator then works through the relationship and reports magnitude |a|, magnitude |b| and dot product.
What does the dot product actually calculate?
It takes angle between vectors (α), x, x, y, y, z, z and cos and converts them into magnitude |a|, magnitude |b| and dot product 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 angle between vectors (α)?
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.
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.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.