Standard normal distribution table (Z-table)

The table gives Φ(z), the probability that Z ≤ z. The row is the first decimal and the column the second: Φ(1.96) is in row 1.9, column .06.

Values of Φ(z)

$z$	$.00$	$.01$	$.02$	$.03$	$.04$	$.05$	$.06$	$.07$	$.08$	$.09$
$0.0$	$0.5000$	$0.5040$	$0.5080$	$0.5120$	$0.5160$	$0.5199$	$0.5239$	$0.5279$	$0.5319$	$0.5359$
$0.1$	$0.5398$	$0.5438$	$0.5478$	$0.5517$	$0.5557$	$0.5596$	$0.5636$	$0.5675$	$0.5714$	$0.5753$
$0.2$	$0.5793$	$0.5832$	$0.5871$	$0.5910$	$0.5948$	$0.5987$	$0.6026$	$0.6064$	$0.6103$	$0.6141$
$0.3$	$0.6179$	$0.6217$	$0.6255$	$0.6293$	$0.6331$	$0.6368$	$0.6406$	$0.6443$	$0.6480$	$0.6517$
$0.4$	$0.6554$	$0.6591$	$0.6628$	$0.6664$	$0.6700$	$0.6736$	$0.6772$	$0.6808$	$0.6844$	$0.6879$
$0.5$	$0.6915$	$0.6950$	$0.6985$	$0.7019$	$0.7054$	$0.7088$	$0.7123$	$0.7157$	$0.7190$	$0.7224$
$0.6$	$0.7257$	$0.7291$	$0.7324$	$0.7357$	$0.7389$	$0.7422$	$0.7454$	$0.7486$	$0.7517$	$0.7549$
$0.7$	$0.7580$	$0.7611$	$0.7642$	$0.7673$	$0.7704$	$0.7734$	$0.7764$	$0.7794$	$0.7823$	$0.7852$
$0.8$	$0.7881$	$0.7910$	$0.7939$	$0.7967$	$0.7995$	$0.8023$	$0.8051$	$0.8078$	$0.8106$	$0.8133$
$0.9$	$0.8159$	$0.8186$	$0.8212$	$0.8238$	$0.8264$	$0.8289$	$0.8315$	$0.8340$	$0.8365$	$0.8389$
$1.0$	$0.8413$	$0.8438$	$0.8461$	$0.8485$	$0.8508$	$0.8531$	$0.8554$	$0.8577$	$0.8599$	$0.8621$
$1.1$	$0.8643$	$0.8665$	$0.8686$	$0.8708$	$0.8729$	$0.8749$	$0.8770$	$0.8790$	$0.8810$	$0.8830$
$1.2$	$0.8849$	$0.8869$	$0.8888$	$0.8907$	$0.8925$	$0.8944$	$0.8962$	$0.8980$	$0.8997$	$0.9015$
$1.3$	$0.9032$	$0.9049$	$0.9066$	$0.9082$	$0.9099$	$0.9115$	$0.9131$	$0.9147$	$0.9162$	$0.9177$
$1.4$	$0.9192$	$0.9207$	$0.9222$	$0.9236$	$0.9251$	$0.9265$	$0.9279$	$0.9292$	$0.9306$	$0.9319$
$1.5$	$0.9332$	$0.9345$	$0.9357$	$0.9370$	$0.9382$	$0.9394$	$0.9406$	$0.9418$	$0.9429$	$0.9441$
$1.6$	$0.9452$	$0.9463$	$0.9474$	$0.9484$	$0.9495$	$0.9505$	$0.9515$	$0.9525$	$0.9535$	$0.9545$
$1.7$	$0.9554$	$0.9564$	$0.9573$	$0.9582$	$0.9591$	$0.9599$	$0.9608$	$0.9616$	$0.9625$	$0.9633$
$1.8$	$0.9641$	$0.9649$	$0.9656$	$0.9664$	$0.9671$	$0.9678$	$0.9686$	$0.9693$	$0.9699$	$0.9706$
$1.9$	$0.9713$	$0.9719$	$0.9726$	$0.9732$	$0.9738$	$0.9744$	$0.9750$	$0.9756$	$0.9761$	$0.9767$
$2.0$	$0.9772$	$0.9778$	$0.9783$	$0.9788$	$0.9793$	$0.9798$	$0.9803$	$0.9808$	$0.9812$	$0.9817$
$2.1$	$0.9821$	$0.9826$	$0.9830$	$0.9834$	$0.9838$	$0.9842$	$0.9846$	$0.9850$	$0.9854$	$0.9857$
$2.2$	$0.9861$	$0.9864$	$0.9868$	$0.9871$	$0.9875$	$0.9878$	$0.9881$	$0.9884$	$0.9887$	$0.9890$
$2.3$	$0.9893$	$0.9896$	$0.9898$	$0.9901$	$0.9904$	$0.9906$	$0.9909$	$0.9911$	$0.9913$	$0.9916$
$2.4$	$0.9918$	$0.9920$	$0.9922$	$0.9925$	$0.9927$	$0.9929$	$0.9931$	$0.9932$	$0.9934$	$0.9936$
$2.5$	$0.9938$	$0.9940$	$0.9941$	$0.9943$	$0.9945$	$0.9946$	$0.9948$	$0.9949$	$0.9951$	$0.9952$
$2.6$	$0.9953$	$0.9955$	$0.9956$	$0.9957$	$0.9959$	$0.9960$	$0.9961$	$0.9962$	$0.9963$	$0.9964$
$2.7$	$0.9965$	$0.9966$	$0.9967$	$0.9968$	$0.9969$	$0.9970$	$0.9971$	$0.9972$	$0.9973$	$0.9974$
$2.8$	$0.9974$	$0.9975$	$0.9976$	$0.9977$	$0.9977$	$0.9978$	$0.9979$	$0.9979$	$0.9980$	$0.9981$
$2.9$	$0.9981$	$0.9982$	$0.9982$	$0.9983$	$0.9984$	$0.9984$	$0.9985$	$0.9985$	$0.9986$	$0.9986$
$3.0$	$0.9987$	$0.9987$	$0.9987$	$0.9988$	$0.9988$	$0.9989$	$0.9989$	$0.9989$	$0.9990$	$0.9990$
$3.1$	$0.9990$	$0.9991$	$0.9991$	$0.9991$	$0.9992$	$0.9992$	$0.9992$	$0.9992$	$0.9993$	$0.9993$
$3.2$	$0.9993$	$0.9993$	$0.9994$	$0.9994$	$0.9994$	$0.9994$	$0.9994$	$0.9995$	$0.9995$	$0.9995$
$3.3$	$0.9995$	$0.9995$	$0.9995$	$0.9996$	$0.9996$	$0.9996$	$0.9996$	$0.9996$	$0.9996$	$0.9997$
$3.4$	$0.9997$	$0.9997$	$0.9997$	$0.9997$	$0.9997$	$0.9997$	$0.9997$	$0.9997$	$0.9997$	$0.9998$

Critical values (two-sided)

Expression	Equals
$90%$	$z = 1.645$
$95%$	$z = 1.960$
$99%$	$z = 2.576$

Rules

Expression	Equals
$Z$	$\frac{X - μ}{σ}$
$P (Z \leq z)$	$Φ (z)$
$P (Z > z)$	$1 - Φ (z)$
$Φ (- z)$	$1 - Φ (z)$
$P (a < Z < b)$	$Φ (b) - Φ (a)$
$P (∣ Z ∣ < z)$	$2Φ (z) - 1$

Notes

For a negative value use symmetry: Φ(−z) = 1 − Φ(z). For example Φ(−1) = 1 − 0.8413 = 0.1587.

For a general normal variable, standardise first: z = (x − μ)/σ, then read the table.

Every value is computed and checked against published values, rounded to four decimals.