A new analytical model, derived rigorously from scalar diffraction theory, accurately fits soft-x-ray measurements of symmetrical profile gold transmission gratings in all diffracted orders. The calibration system selects numerous photon energies by use of a high-resolution grazing-incidence monochromator and a dc e-beam source. Fine-period free-standing gratings exhibit limited performance and require such testing to determine parameters of and select acceptable gratings for use in time-resolved (0.25 ns) spectrographs of known radiometric response. Unfolded spectra yield a Z-pinch plasma peak kT approximately 250 eV, total radiated energy approximately 900 kJ, and a pinch-driven gold-wall hohlraum Planckian kT approximately 86 eV.