Harmonic Number Calculator
Use this harmonic number calculator to determine the nᵗʰ harmonic number.
H(10)2.928968254
Approximation ln n + γ2.9298007579accurate to about 1/(12n²)
Difference-0.000832503927
ln n2.302585093
Euler–Mascheroni γ0.577215664902
Last term added0.1
The formula
Hₙ = 1 + 1⁄2 + 1⁄3 + … + 1⁄n
It diverges, but slowly
The harmonic series grows without limit, yet only like ln n. Reaching a sum of 10 takes about 12,367 terms; reaching 100 would take more terms than there are atoms in a person. The gap between Hₙ and ln n approaches the Euler–Mascheroni constant γ ≈ 0.5772, whose irrationality is still unproved.