The paper deals with the determination of the discharge coefficient, effective head and newly the limit head in the Kindsvater-Shen formula for the determination of a relatively small discharge of clear water using a thin-plate weir with a triangular notch. The determination of the discharge coefficient, effective head and limit head is based on extensive experimental research and is verified by previous measurements by other authors. The experimental research was characterised by a large range of notch angles (from 5.25° to 91.17°), weir heights (from 0.00 m to 0.20 m), and water temperatures (from 15 °C to 45 °C), as well as a focus on relatively small heads (from 0.02 m to 0.18 m), which is where the strengths of the Kindsvater-Shen formula stand out. The experimental research supplemented existing knowledge about the overflow occurring with small heads and small weir notch angles. The newly determined dependencies in the Kindsvater-Shen formula extended its applicability to weirs with small notch angles and newly enabled the determination of the limit head, which restricts its applicability in the determination of small discharges.