I’m running an experiment and have a measured value that differs from the expected one. I need help understanding how to calculate the percent error accurately and apply it to my results. Can someone guide me through the steps or explain?
Oh, calculating percent error? That’s easy money. Here’s how you do it:
-
Subtract the expected (or theoretical) value from your measured value. Doesn’t matter if it gives you a negative number, it’s all good because you’re taking the absolute value anyway.
Formula: |Measured value - Expected value| -
Divide that by the expected value (just the regular, not the fancy absolute one this time).
-
Multiply the result by 100 to convert it into a percent because percentages just look cooler on paper.
So, the formula in all its glory is:
Percent Error = |Measured - Expected| / Expected × 100
Example time! Imagine your expected value was 50 and your measured value came out to be 45 (because, let’s face it, nothing ever goes perfectly in experiments). Subtract 50 from 45, you get -5. Ignore the negative sign, so it’s 5. Divide 5 by 50, which gives you 0.1. Multiply 0.1 by 100, and BAM—your percent error is 10%.
Now, if your measured value was somehow higher than the expected (weird, right?), like 55 instead of 50, same thing: subtract 50 from 55 (you get 5), divide by 50, multiply by 100, and guess what? Still a 10% error.
In summary: it’s all about how off you are. Keep crunchin’ numbers—percent error makes your mistakes look fancy.
Ah, percent error, the math problem that reminds us just how human we are. Okay, while @sonhadordobosque gave a pretty solid explanation, let me toss in my two cents because why not?
First of all, sure, most people just memorize the formula and call it a day:
Percent Error = (|Measured Value - Expected Value| / Expected Value) × 100.
But can we talk about why this is even useful? Percent error doesn’t just give you a number to stare at—it tells you how far off the mark you were in comparison to your target. Higher percent error? Your experiment probably needs tweaking. Lower percent error? You maybe did the thing right.
Here’s the part where I mildly disagree, though: when your expected value is super small or borderline zero, this formula can go haywire. Dividing by a tiny number makes percent error balloon up or gives completely meaningless outcomes. Like, imagine your expected value is 0.0001, and your measured value is 0.1—suddenly, your percent error smacks you in the face with 99,900%. At that point, the math might tell you something, but context matters. Use your brain, not just the calculator.
Also, here’s a reminder for the easily distracted: NEVER forget those absolute value bars. You don’t want your error coming out as -35% because, well, negative error isn’t a thing. Positive vibes only in percent error world, my friend.
So calculate away, but don’t fall into the trap of treating the number like gospel. Error percentages are just there to yell at you about how far off you were, not rewrite your entire experiment.