Estimating the area density of the phasic interface represents an important step for phase-change rate calculations. In the context of volume-of-fluid methods, algebraic methods based on the norm of the volume-fraction gradient are usually employed, resulting either in the smearing of the interface or in area underestimation. Conversely, methods based on interface reconstruction require complex geometric calculations. In this work, we present a novel algorithm for interfacial area density calculation, the Marker Gradient method. It preserves the simplicity and robustness of algebraic gradient calculations; nevertheless, the interface is represented in a sharp manner. We show that the number of discretization points governs the accuracy of the algorithm and the error in calculated area is minor if a sufficient number of points is used. We verify the method on a three-dimensional Cartesian mesh for static and moving spheres as well as for bubble growth in a quiescent superheated liquid. For validation, growth of a rising bubble is simulated. We compare the results to more complex approaches and show that the error of the Marker Gradient method is negligible at practical grid resolutions. As the extension of the presented method to unstructured meshes is straightforward thanks to its simplicity, this work represents another step for development of high-fidelity simulation tools for problems involving phase transition in non-trivial geometries.