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The WMAP mission has produced sky maps from seven years of observations at L2. We present the angular power spectra derived from the seven-year maps and discuss the cosmological conclusions that can be inferred from WMAP data alone. With the seven-year data, the temperature (TT) spectrum measurement has a signal-to-noise ratio per multipole that exceeds unity for l< 919; and in band powers of width Δl= 10, the signal-to-noise ratio exceeds unity up to l= 1060. The third acoustic peak in the TT spectrum is now well measured by WMAP. In the context of a flat ΛCDM model, this improvement allows us to place tighter constraints on the matter density from WMAP data alone, Ω m h 2= 0.1334+ 0.0056− 0.0055, and on the epoch of matter-radiation equality, z eq= 3196+ 134− 133. The temperature-polarization (TE) spectrum is detected in the seven-year data with a significance of 20σ, compared to 13σ with …