A method for performing an adaptive differentially private count operation on a set of data stored by a database, the method comprising: receiving a request from a client device to perform a query on the set of data stored by the database, wherein the request identifies a target accuracy and a maximum privacy spend, wherein the target accuracy comprises a maximum relative error, and the maximum privacy spend comprises a value of a privacy parameter ε describing a degree of information released about the set of data due to the query; performing, responsive to receiving the request to perform the query, a differentially private count operation on the set of data to produce a differentially private result, the differentially private count operation comprising: performing a count operation on the set of data to produce a result; perturbing the result to produce a differentially private result using a noise value sampled from a Laplace distribution and based on a fractional privacy spend comprising a fraction of the maximum privacy spend; and iteratively calibrating the noise value of the differentially private result using a secondary distribution different from the Laplace distribution and a new fractional privacy spend until at least one of: an iteration uses the maximum privacy spend, and a relative error of the differentially private result is determined to satisfy the target accuracy; and sending, to the client device, the differentially private result. receiving a request from a client device to perform a query on the set of data stored by the database, wherein the request identifies a target accuracy and a maximum privacy spend, wherein the target accuracy comprises a maximum relative error, and the maximum privacy spend comprises a value of a privacy parameter ε describing a degree of information released about the set of data due to the query; performing, responsive to receiving the request to perform the query, a differentially private count operation on the set of data to produce a differentially private result, the differentially private count operation comprising: performing a count operation on the set of data to produce a result; perturbing the result to produce a differentially private result using a noise value sampled from a Laplace distribution and based on a fractional privacy spend comprising a fraction of the maximum privacy spend; and iteratively calibrating the noise value of the differentially private result using a secondary distribution different from the Laplace distribution and a new fractional privacy spend until at least one of: an iteration uses the maximum privacy spend, and a relative error of the differentially private result is determined to satisfy the target accuracy; and sending, to the client device, the differentially private result. performing a count operation on the set of data to produce a result; perturbing the result to produce a differentially private result using a noise value sampled from a Laplace distribution and based on a fractional privacy spend comprising a fraction of the maximum privacy spend; and iteratively calibrating the noise value of the differentially private result using a secondary distribution different from the Laplace distribution and a new fractional privacy spend until at least one of: an iteration uses the maximum privacy spend, and a relative error of the differentially private result is determined to satisfy the target accuracy; and sending, to the client device, the differentially private result. an iteration uses the maximum privacy spend, and a relative error of the differentially private result is determined to satisfy the target accuracy; and sending, to the client device, the differentially private result.