A sponsor specifies a content campaign along with a budget, a duration, a maximum bid value and one or more objectives associated with the content campaign. An online system presenting the sponsored content calibrates the pacing factor of the content campaign to present the sponsored content evenly throughout the specified duration of the campaign. Paced bids are provided for the content campaign to compete for placement in opportunities during a ramp-up period, in which the paced bid associated with the campaign is adjusted to the maximum bid value. The target-ramp up period is iteratively determined as the current paced bid approaches the maximum bid value to avoid overspending the budget early in the campaign. When a conversion event occurs, the ramp-up period ends and the content campaign transitions to a normal pacing algorithm.