Error Function Calculator

Enter a value for x:

The Error Function Calculator is a tool that calculates the error function (erf) for a given number.

What is the Error Function?

The error function is a special mathematical function that has a shape like a curve or “S”. It is often used in probability, statistics, and equations in science and engineering. It is also known as the Gauss error function or probability integral.

How is the Error Function Defined?

The error function is mathematically defined by the following formula:

erf(x) = $erf(x) = (2/sqrt(pi)) ∫ e^(-t^2) dt$

Where:

x is the input number,
π (pi) is the constant (~3.14159),
e is the exponential function (~2.71828).

The error function calculates the probability that a value lies within a specific range.

Error Function Table

The following table shows the values of the error function (erf(x)) and the complementary error function (erfc(x)) for numbers between 0 and 3.5, with an increment of 0.01:

x	erf(x)	erfc(x)
0.0	0.0	1.0
0.01	0.011283416	0.988716584
0.02	0.022564575	0.977435425
0.03	0.033841222	0.966158778
0.04	0.045111106	0.954888894
0.05	0.056371978	0.943628022
0.06	0.067621594	0.932378406
0.07	0.07885772	0.92114228
0.08	0.090078126	0.909921874
0.09	0.101280594	0.898719406
0.1	0.112462916	0.887537084
0.11	0.123622896	0.876377104
0.12	0.134758352	0.865241648
0.13	0.145867115	0.854132885
0.14	0.156947033	0.843052967
0.15	0.167995971	0.832004029
0.16	0.179011813	0.820988187
0.17	0.189992461	0.810007539
0.18	0.200935839	0.799064161
0.19	0.211839892	0.788160108
0.2	0.222702589	0.777297411
0.21	0.233521923	0.766478077
0.22	0.244295912	0.755704088
0.23	0.2550226	0.7449774
0.24	0.265700059	0.734299941
0.25	0.27632639	0.72367361
0.26	0.286899723	0.713100277
0.27	0.297418219	0.702581781
0.28	0.307880068	0.692119932
0.29	0.318283496	0.681716504
0.3	0.328626759	0.671373241
0.31	0.33890815	0.66109185
0.32	0.349125995	0.650874005
0.33	0.359278655	0.640721345
0.34	0.369364529	0.630635471
0.35	0.379382054	0.620617946
0.36	0.389329701	0.610670299
0.37	0.399205984	0.600794016
0.38	0.409009453	0.590990547
0.39	0.4187387	0.5812613
0.4	0.428392355	0.571607645
0.41	0.43796909	0.56203091
0.42	0.447467618	0.552532382
0.43	0.456886695	0.543113305
0.44	0.466225115	0.533774885
0.45	0.47548172	0.52451828
0.46	0.48465539	0.51534461
0.47	0.493745051	0.506254949
0.48	0.502749671	0.497250329
0.49	0.511668261	0.488331739
0.5	0.520499878	0.479500122
0.51	0.52924362	0.47075638
0.52	0.53789863	0.46210137
0.53	0.546464097	0.453535903
0.54	0.55493925	0.44506075
0.55	0.563323366	0.436676634
0.56	0.571615764	0.428384236
0.57	0.579815806	0.420184194
0.58	0.5879229	0.4120771
0.59	0.595936497	0.404063503
0.6	0.603856091	0.396143909
0.61	0.611681219	0.388318781
0.62	0.619411462	0.380588538
0.63	0.627046443	0.372953557
0.64	0.634585829	0.365414171
0.65	0.642029327	0.357970673
0.66	0.649376688	0.350623312
0.67	0.656627702	0.343372298
0.68	0.663782203	0.336217797
0.69	0.670840062	0.329159938
0.7	0.677801194	0.322198806
0.71	0.68466555	0.31533445
0.72	0.691433123	0.308566877
0.73	0.698103943	0.301896057
0.74	0.704678078	0.295321922
0.75	0.711155634	0.288844366
0.76	0.717536753	0.282463247
0.77	0.723821614	0.276178386
0.78	0.730010431	0.269989569
0.79	0.736103454	0.263896546
0.8	0.742100965	0.257899035
0.81	0.748003281	0.251996719
0.82	0.753810751	0.246189249
0.83	0.759523757	0.240476243
0.84	0.765142711	0.234857289
0.85	0.770668058	0.229331942
0.86	0.776100268	0.223899732
0.87	0.781439845	0.218560155
0.88	0.786687319	0.213312681
0.89	0.791843247	0.208156753
0.9	0.796908212	0.203091788
0.91	0.801882826	0.198117174
0.92	0.806767722	0.193232278
0.93	0.811563559	0.188436441
0.94	0.816271019	0.183728981
0.95	0.820890807	0.179109193
0.96	0.82542365	0.17457635
0.97	0.829870293	0.170129707
0.98	0.834231504	0.165768496
0.99	0.83850807	0.16149193
1.0	0.842700793	0.157299207
1.01	0.846810496	0.153189504
1.02	0.850838018	0.149161982
1.03	0.854784211	0.145215789
1.04	0.858649947	0.141350053
1.05	0.862436106	0.137563894
1.06	0.866143587	0.133856413
1.07	0.869773297	0.130226703
1.08	0.873326158	0.126673842
1.09	0.876803102	0.123196898
1.1	0.88020507	0.11979493
1.11	0.883533012	0.116466988
1.12	0.88678789	0.11321211
1.13	0.88997067	0.11002933
1.14	0.893082328	0.106917672
1.15	0.896123843	0.103876157
1.16	0.899096203	0.100903797
1.17	0.902000399	0.097999601
1.18	0.904837427	0.095162573
1.19	0.907608286	0.092391714
1.2	0.910313978	0.089686022
1.21	0.912955508	0.087044492
1.22	0.915533881	0.084466119
1.23	0.918050104	0.081949896
1.24	0.920505184	0.079494816
1.25	0.922900128	0.077099872
1.26	0.925235942	0.074764058
1.27	0.927513629	0.072486371
1.28	0.929734193	0.070265807
1.29	0.931898633	0.068101367
1.3	0.934007945	0.065992055
1.31	0.936063123	0.063936877
1.32	0.938065155	0.061934845
1.33	0.940015026	0.059984974
1.34	0.941913715	0.058086285
1.35	0.943762196	0.056237804
1.36	0.945561437	0.054438563
1.37	0.947312398	0.052687602
1.38	0.949016035	0.050983965
1.39	0.950673296	0.049326704
1.4	0.95228512	0.04771488
1.41	0.953852439	0.046147561
1.42	0.955376179	0.044623821
1.43	0.956857253	0.043142747
1.44	0.95829657	0.04170343
1.45	0.959695026	0.040304974
1.46	0.96105351	0.03894649
1.47	0.9623729	0.0376271
1.48	0.963654065	0.036345935
1.49	0.964897865	0.035102135
1.5	0.966105146	0.033894854
1.51	0.967276748	0.032723252
1.52	0.968413497	0.031586503
1.53	0.969516209	0.030483791
1.54	0.97058569	0.02941431
1.55	0.971622733	0.028377267
1.56	0.972628122	0.027371878
1.57	0.973602627	0.026397373
1.58	0.974547009	0.025452991
1.59	0.975462016	0.024537984
1.6	0.976348383	0.023651617
1.61	0.977206837	0.022793163
1.62	0.978038088	0.021961912
1.63	0.97884284	0.02115716
1.64	0.97962178	0.02037822
1.65	0.980375585	0.019624415
1.66	0.981104921	0.018895079
1.67	0.981810442	0.018189558
1.68	0.982492787	0.017507213
1.69	0.983152587	0.016847413
1.7	0.983790459	0.016209541
1.71	0.984407008	0.015592992
1.72	0.985002827	0.014997173
1.73	0.9855785	0.0144215
1.74	0.986134595	0.013865405
1.75	0.986671671	0.013328329
1.76	0.987190275	0.012809725
1.77	0.987690942	0.012309058
1.78	0.988174196	0.011825804
1.79	0.988640549	0.011359451
1.8	0.989090502	0.010909498
1.81	0.989524545	0.010475455
1.82	0.989943156	0.010056844
1.83	0.990346805	0.009653195
1.84	0.990735948	0.009264052
1.85	0.99111103	0.00888897
1.86	0.991472488	0.008527512
1.87	0.991820748	0.008179252
1.88	0.992156223	0.007843777
1.89	0.992479318	0.007520682
1.9	0.992790429	0.007209571
1.91	0.99308994	0.00691006
1.92	0.993378225	0.006621775
1.93	0.99365565	0.00634435
1.94	0.993922571	0.006077429
1.95	0.994179334	0.005820666
1.96	0.994426275	0.005573725
1.97	0.994663725	0.005336275
1.98	0.994892	0.005108
1.99	0.995111413	0.004888587
2.0	0.995322265	0.004677735
2.01	0.995524849	0.004475151
2.02	0.995719451	0.004280549
2.03	0.995906348	0.004093652
2.04	0.99608581	0.00391419
2.05	0.996258096	0.003741904
2.06	0.996423462	0.003576538
2.07	0.996582153	0.003417847
2.08	0.996734409	0.003265591
2.09	0.996880461	0.003119539
2.1	0.997020533	0.002979467
2.11	0.997154845	0.002845155
2.12	0.997283607	0.002716393
2.13	0.997407023	0.002592977
2.14	0.997525293	0.002474707
2.15	0.997638607	0.002361393
2.16	0.997747152	0.002252848
2.17	0.997851108	0.002148892
2.18	0.997950649	0.002049351
2.19	0.998045943	0.001954057
2.2	0.998137154	0.001862846
2.21	0.998224438	0.001775562
2.22	0.998307948	0.001692052
2.23	0.998387832	0.001612168
2.24	0.998464231	0.001535769
2.25	0.998537283	0.001462717
2.26	0.998607121	0.001392879
2.27	0.998673872	0.001326128
2.28	0.998737661	0.001262339
2.29	0.998798606	0.001201394
2.3	0.998856823	0.001143177
2.31	0.998912423	0.001087577
2.32	0.998965513	0.001034487
2.33	0.999016195	0.000983805
2.34	0.99906457	0.00093543
2.35	0.999110733	0.000889267
2.36	0.999154777	0.000845223
2.37	0.99919679	0.00080321
2.38	0.999236858	0.000763142
2.39	0.999275064	0.000724936
2.4	0.999311486	0.000688514
2.41	0.999346202	0.000653798
2.42	0.999379283	0.000620717
2.43	0.999410802	0.000589198
2.44	0.999440826	0.000559174
2.45	0.99946942	0.00053058
2.46	0.999496646	0.000503354
2.47	0.999522566	0.000477434
2.48	0.999547236	0.000452764
2.49	0.999570712	0.000429288
2.5	0.999593048	0.000406952
2.51	0.999614295	0.000385705
2.52	0.999634501	0.000365499
2.53	0.999653714	0.000346286
2.54	0.999671979	0.000328021
2.55	0.99968934	0.00031066
2.56	0.999705837	0.000294163
2.57	0.999721511	0.000278489
2.58	0.9997364	0.0002636
2.59	0.999750539	0.000249461
2.6	0.999763966	0.000236034
2.61	0.999776711	0.000223289
2.62	0.999788809	0.000211191
2.63	0.999800289	0.000199711
2.64	0.999811181	0.000188819
2.65	0.999821512	0.000178488
2.66	0.999831311	0.000168689
2.67	0.999840601	0.000159399
2.68	0.999849409	0.000150591
2.69	0.999857757	0.000142243
2.7	0.999865667	0.000134333
2.71	0.999873162	0.000126838
2.72	0.999880261	0.000119739
2.73	0.999886985	0.000113015
2.74	0.999893351	0.000106649
2.75	0.999899378	0.000100622
2.76	0.999905082	9.4918e-05
2.77	0.99991048	8.952e-05
2.78	0.999915587	8.4413e-05
2.79	0.999920418	7.9582e-05
2.8	0.999924987	7.5013e-05
2.81	0.999929307	7.0693e-05
2.82	0.99993339	6.661e-05
2.83	0.99993725	6.275e-05
2.84	0.999940898	5.9102e-05
2.85	0.999944344	5.5656e-05
2.86	0.999947599	5.2401e-05
2.87	0.999950673	4.9327e-05
2.88	0.999953576	4.6424e-05
2.89	0.999956316	4.3684e-05
2.9	0.999958902	4.1098e-05
2.91	0.999961343	3.8657e-05
2.92	0.999963645	3.6355e-05
2.93	0.999965817	3.4183e-05
2.94	0.999967866	3.2134e-05
2.95	0.999969797	3.0203e-05
2.96	0.999971618	2.8382e-05
2.97	0.999973334	2.6666e-05
2.98	0.999974951	2.5049e-05
2.99	0.999976474	2.3526e-05
3.0	0.99997791	2.209e-05
3.01	0.999979261	2.0739e-05
3.02	0.999980534	1.9466e-05
3.03	0.999981732	1.8268e-05
3.04	0.999982859	1.7141e-05
3.05	0.99998392	1.608e-05
3.06	0.999984918	1.5082e-05
3.07	0.999985857	1.4143e-05
3.08	0.99998674	1.326e-05
3.09	0.999987571	1.2429e-05
3.1	0.999988351	1.1649e-05
3.11	0.999989085	1.0915e-05
3.12	0.999989774	1.0226e-05
3.13	0.999990422	9.578e-06
3.14	0.99999103	8.97e-06
3.15	0.999991602	8.398e-06
3.16	0.999992138	7.862e-06
3.17	0.999992642	7.358e-06
3.18	0.999993115	6.885e-06
3.19	0.999993558	6.442e-06
3.2	0.999993974	6.026e-06
3.21	0.999994365	5.635e-06
3.22	0.999994731	5.269e-06
3.23	0.999995074	4.926e-06
3.24	0.999995396	4.604e-06
3.25	0.999995697	4.303e-06
3.26	0.99999598	4.02e-06
3.27	0.999996245	3.755e-06
3.28	0.999996493	3.507e-06
3.29	0.999996725	3.275e-06
3.3	0.999996942	3.058e-06
3.31	0.999997146	2.854e-06
3.32	0.999997336	2.664e-06
3.33	0.999997515	2.485e-06
3.34	0.999997681	2.319e-06
3.35	0.999997838	2.162e-06
3.36	0.999997983	2.017e-06
3.37	0.99999812	1.88e-06
3.38	0.999998247	1.753e-06
3.39	0.999998367	1.633e-06
3.4	0.999998478	1.522e-06
3.41	0.999998582	1.418e-06
3.42	0.999998679	1.321e-06
3.43	0.99999877	1.23e-06
3.44	0.999998855	1.145e-06
3.45	0.999998934	1.066e-06
3.46	0.999999008	9.92e-07
3.47	0.999999077	9.23e-07
3.48	0.999999141	8.59e-07
3.49	0.999999201	7.99e-07
3.5	0.999999257	7.43e-07