Code-modulated embedded test (CoMET) has been investigated for simultaneous testing and calibration of phased-array elements using phase-shifter modulation and a single scalar detector together with an off-line equation solver. To improve the speed and reduce the complexity of the calibration, this work presents a revised methodology relying only on correlations and eliminating equation solvers within the calibration loop. The new technique, “beamformer calibration using coded correlations” (BC3), operates by calibrating the phased-array's in-phase and quadrature-phase correlations between elements. Within BC3, a first method calibrates the array's response by using two two-dimensional (2-D) correlations. A second method further reduces the total calibration time and improves accuracy by using two one-dimensional (1-D) correlations together with an empirical model to predict gain-dependent phase variation. Also, we investigate ways to improve the speed of calibration by reducing the code length and the number of searching states per iteration. The phase and gain accuracy, calibration time, and antenna beam patterns are measured and compared using original and proposed calibration methods on an eight-element receiver at 10 GHz. The most accurate BC3 method achieves 1.4 deg. and 0.23 dB root-mean-squared (RMS) phase and gain error, 1.1 dB maximum gain error and -37.8 dB calculated residual sidelobe level (RSL) for the calibrated array, with 12X speedup compared to CoMET. The fastest BC3 method achieves 2.1 deg. and 0.27 dB root-mean-squared (RMS) phase and gain error, 1.2 dB maximum gain error and -35.3 dB RSL for the array with 33X speedup compared to CoMET.