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Formulation of noniterative mathematical expressions for moist thermodynamics presents a challenge for both numerical and theoretical modellers. This technical note offers a simple and efficient tool for approximating two common thermodynamic relationships: temperature, T, at a given pressure, P, along a saturated adiabat, T(P, theta(w)), as well as its corresponding inverse form theta(w)(P, T), where theta(w) is wet-bulb potential temperature. Our method allows direct calculation of T(P, theta(w)) and theta(w)(P, T) on a thermodynamic domain bounded by -70 <= theta(w) < 40 degrees C, P > 1 kPa and -100 <= T < 40 degrees C, P > 1 kPa, respectively. The proposed parameterizations offer high accuracy (mean absolute errors of 0.016 and 0.002 degrees C for T(P, theta(w)) and theta(w)(P, T), respectively) on a notably larger thermodynamic region than previously studied. The paper includes a method summary and a ready-to-use tool to aid atmospheric physicists in their practical applications.