If your three weeks pregnant will it show a positive test?

It is possible to get a positive pregnancy test 3 weeks after conception. Pregnancy tests detect a hormone called human chorionic gonadotropin (hCG) in your urine. hCG levels can be found as early as days after implantation which usually occurs 7-10 days after ovulation.

So it depends on which point exactly 3 weeks is referring to but on average a pregnancy test could yield a positive result on an accurate home pregnancy test.