Measurement, Units & Errors
Every measurement, units & errors calculator on CalcEngines — each with its formula, a worked example, the standard it follows and the assumptions it makes.
8 calculators in this section
- Absolute, Relative and Percentage Error CalculatorPercentage error has three denominators in common use and they give three different answers. This page computes all three from one pair of values, keeps the sign so you can see whether the instrument reads high or low, and — given the uncertainty on your own measurement — says whether the discrepancy is real or just scatter.
- Dimensional Formula and Homogeneity Check CalculatorBuild a formula as a product of powers of two quantities, name what it is supposed to give, and this page returns the M, L and T exponents of what you actually built, the exponents of the target, and which dimension is out and by how much. A dimensionally wrong equation is always wrong; a right one may still be.
- Error Propagation Calculator: Sums, Products and PowersGive two measured quantities with their uncertainties and the combination you need, and this page returns the uncertainty on the answer, where to cut the figures, and both rules side by side — the simple addition your board marks, and the quadrature of the metrology guide, which on these defaults is 2.13 per cent against 3.00.
- Least Count and Instrument Choice CalculatorLeast count is easy; choosing the instrument is the judgement. Tell this page what you are measuring and how many figures the question wants, and it returns one least count as a percentage of your measurement, the figures that instrument can actually give you on it, and the least count you would need instead.
- Order of Magnitude and Scientific Notation CalculatorOrder of magnitude has two definitions in use — the exponent in scientific notation, and the nearest power of ten — and they disagree for every number whose mantissa is above 3.16. This page gives both, the engineering form with its SI prefix, and how many decades apart two quantities are.
- Screw Gauge and Micrometer Reading Calculator, with Zero ErrorLeast count is the pitch divided by the circular scale divisions, and the reading is the easy part. The trap is a negative zero error: with the circular zero ABOVE the reference line the error is not the division you can see but N minus it, so a reading of 47 on a 50-division head is −0.03 mm and not −0.47 mm.
- Significant Figures and Rounding CalculatorHow many figures is your answer entitled to? Give two measured values and what each was quoted to, and this page returns the figures the result may carry, the rounded answer, and what your board does when the digit you drop is exactly five — NCERT rounds 1.425 to 1.42, the rule most people were taught gives 1.43.
- Vernier Calliper Reading Calculator, with Zero ErrorThe correction, not the reading, is where the marks go. A POSITIVE zero error is subtracted and a NEGATIVE one is added, and a negative zero error is not the division you can see — it is N minus that division. Give this page what you can see and it does both steps, and shows you what the other sign would have cost.