Estimation And Approximation Calculator

Work out estimation and approximation instantly with clear inputs, formula shown and shareable results.

About Estimation And Approximation Calculator

Estimation rounds each value to a few significant figures before calculating, giving a quick sanity check. Comparing with the exact answer shows how much precision the shortcut costs.

Formula

Percentage error

100 × |exact − estimate| / |exact|

Worked example

With the default values below, Estimation And Approximation Calculator returns Estimated product of 1,000.000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First value: 48.7
Second value: 21.3
Round each to this many significant figuresaccepts 1–6: 1

Results

Estimated product: 1,000.000000
Exact product: 1,037.310000
Absolute error: 37.310000
Percentage error: 3.5968 %

Step by step

1Values used
2Percentage error
3Estimated product= 1,000.000000
4Exact product= 1,037.310000
5Absolute error= 37.310000
6Percentage error= 3.5968 %

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

48.7 × 21.3 estimated to 1 significant figure?

50 × 20 = 1000 against the exact 1037.31, a 3.6% error — close enough to catch a gross mistake.

Why estimate at all?

It guards against slips of a factor of ten and gives a feel for whether a computed answer is plausible.