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How do you use this calculator?Just like a real one! The only big difference is that you can click the ± button and then enter the (absolute) uncertainty for that value. What is an uncertainty?In real life, you can't measure something perfectly. Take a moment to think about that. Take a ruler for example - you can measure that a pencil is 15cm long, you can probably measure that it's 15.1cm if you look closely. But can we say that the pencil is 15.100000cm long? No, we can't, because we aren't sure if all those 0's are actually 0, they could be 5's, of 9's or anything! So what can we do about this? This is where uncertainties come in. when we can say that the pencil is 15.1cm long plus or minus 0.05cm! What this means is that the actual length of the pencil could be anywhere between 15.1+0.05cm (15.15cm) and 15.1-0.05cm (15.05cm). In mathematical terms we use the funny ± symbol to mean plus or minus, so our pencil length would be this: 15.01±0.05cm. Now when someone comes along with a fancy new super-ruler, and says "Aha! This pencil isn't 15.1cm long, it's 15.09cm long!" we can still say that we're right, because 15.09 is between 15.05 and 15.15. This is why it's always important to record the uncertainty of things that you measure, because it means that you always know exactly how exact your measurement is (smaller uncertainties mean a more exact measurement). What is "real mode"?The way to calculate uncertainty estimates that I was taught at university was wrong (or at least very simplified for certain uses). By default this calculator still uses this way, as it is what I use it most for, however, by using "real mode" you can calculate more accurate error estimates. The real mode uses a type of mathematics called "interval arithmetic", which bascially means that we are doing maths with ranges of numbers. The actual maths is pretty complicated, and I don't pretend to understand it all, but by standing on the shoulders of giants (Jeff Tian), I have managed to build it into this calculator. In most cases you shouldn't see massive differences, except when dealing with very large errors. It should be noted that real mode is much better at dealing (correctly) with errors in exponents, square roots, logs, and all those more advanced functions. I've found a bug, or have a suggestion!Wonderful! Please send me an email either by filling in the form on my website, or just send me an email at calculator@ollyfg.com. I love hearing about bugs and improvements people want, as it means that this calculator will always be improving. If you yourself know your way around javascript, you can feel free to make changes and submit pull requests to this calculator on Github. |
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