Age of Consent
The Age of Consent in New Hampshire is 18, per RSA 457:5:
The age of consent shall be in the male and in the female, 18 years. Any marriage contracted by a person below the age of consent, except as hereinafter provided, may in the discretion of the superior court be annulled at the suit of the party who at the time of contracting such marriage was below the age of consent, or at the suit of his or her parent or guardian, unless such party after arriving at such age shall have confirmed the marriage.
For contracting marriage, one must be 16 per RSA 457:4:
No person below the age of 16 years shall be capable of contracting a valid marriage, and all marriages contracted by such persons shall be null and void.
For such cases, see extra details in RSA 457:6.
Romeo and Juliet
Despite the age of consent being 18, there is a "Romeo and Juliet" law. According to RSA 532-A:3:
A person is guilty of a class B felony if such person: [...]
II. Engages in sexual penetration with a person who is 13 years of age or older and under 16 years of age where the age difference between the actor and the other person is 4 years or more;
The law goes on to describe further situations, many of which have exemptions for people who are within 4 years of age of the victim. If you're in a situation where you're actively looking this up, I might advise you hit the brakes and wait for marriage.