➗ Harmonic Series Calculator
Calculate the sum of the first n terms of the harmonic series (1 + 1/2 + 1/3 + … + 1/n).
What the Harmonic Series Is
The harmonic series is the sum 1 + 1/2 + 1/3 + 1/4 + … and so on. Even though each term gets smaller, the full infinite series actually diverges (grows without bound) — just extremely slowly. This calculator computes the partial sum up to whatever term count you choose.
The Formula
Hn = ∑k=1n (1/k). For large n, this sum is closely approximated by ln(n) + γ, where γ (the Euler-Mascheroni constant) is approximately 0.5772156649.
This calculator caps the term count at 1,000,000 to keep results computing quickly in your browser. It’s provided for math and computer science education and general curiosity.
Last reviewed August 2026