z, z′, ζ and En calculator
Score a PT result and see its band, with the working shown. Free, no sign-up. Everything runs in your browser; nothing you enter is sent or stored.
Score calculator
Change the numbers or drag the slider. Add uncertainties to see z′, ζ and En.
(5.71 − 5.20) / 0.20 = +2.55
Add uncertainties
| z′ u(xpt) ≤ 0.3 σpt, so z is enough here | +2.54 | Questionable |
| ζ uses u(x) and u(xpt) | +3.39 | Unsatisfactory |
| En U = 2u (k = 2); satisfactory when |En| ≤ 1 | +1.69 | Unsatisfactory |
How it works
z compares your result x with the assigned value xpt in units of σpt: z = (x − xpt) / σpt. The sign says high or low. |z| ≤ 2.0 is satisfactory, 2.0 < |z| < 3.0 questionable and |z| ≥ 3.0 unsatisfactory.
z′ adds the uncertainty of the assigned value. Use it when u(xpt) is more than 0.3 σpt; it has the same limits as z.
ζ uses your own standard uncertainty u(x) and u(xpt) instead of σpt, with the same limits. En uses expanded uncertainties (this calculator takes U = 2u); |En| ≤ 1.0 is satisfactory.
Your scheme's plan decides which score and which limits apply, and how many decimals are reported.
For learning and for checking your own arithmetic. Your scheme's report and rules are what count.