Data from a network of seismometers, a tiltmeter and the pattern of summit inflation between eruptions have made qualitative eruption forecasting possible on Kilauea volcano for over 20 years. This paper formulates quantitative forecasting by calculating the probability of an eruption based on current levels of tilt, tilt rate, seismicity, and fortnightly tide. Plots of eruption probability as a function of various parameters are derived using a set of 29 eruptions during 1959–1979. The method tests the precursory significance of various parameters over different time scales and determines probabilities by comparing data before eruptions with data values generally. Tilt level is an eruption precursor significant to better than 99.9% when averaged over any interval from 1 to 20 days. Tilt rate is a precursor significant to better than 99.999%, but noise in the data requires that it be averaged over 30 days or more. Earthquakes are a short‐term precursor significant to better than 99% when averaged over 1–10 days for larger earthquakes near the summit caldera and over 5–20 days for very small earthquakes within the caldera. The fortnightly modulation of tides influences eruption probability and has a precursory significance of 97%. Probabilities are independent of the time elapsed since the last eruption. The eruption probability, when tested against the eruption record from which it was derived, is significant to the 99.98% level when compared with random guessing. Ongoing 1‐day, 7‐day, and 30‐day forecasts are calculated by computer at the Hawaiian Volcano Observatory and supplement the qualitative interpretation of geophysical data.