Inclusion Criteria:  A diagnosis of PAH group 4 or group 1 in any of the following subtypes:  Idiopathic PAH (iPAH) Heritable PAH (hPAH) Connective tissue disease associated PAH (aPAH) In case of PAH in group 4, no further invasive treatment including pulmonary endarterectomy or pulmonary balloon angioplasty must be planned at time of inclusion. Symptomatic PAH in WHO functional class II-III as assessed by the screening clinician. Clinically stable patients on pulmonary vasodilator treatment with PDE5i, ERA, PA/IPA alone or in combination without considerations from the treating physician team towards treatment escalation and a treatment duration of at least four weeks. Clinical stability defined as stable symptoms without progression as assessed by treating clinician and without the need for unplanned hospital admissions due to worsening PAH within three months of screening. Fertile women (< 50 years of age) must use safe contraceptives (Intra uterine device or hormonal contraception) for the duration of the study and have a negative pregnancy test Able to understand the written patient information in Danish and give informed consent. Age ≥ 18 years Ability to perform cardio pulmonary exercise test  Exclusion Criteria:  Known allergy to the study medication Treatment with an SGLT2i within 6 months prior to baseline Type 1 or type 2 diabetes Impaired renal function with an eGFR < 30 mL/min/m2 within four weeks of screening Severe liver dysfunction (Child-Pugh class c) Listed for lung transplantation at the time of screening Planned initiation of iv prostacyclin therapy/ IPA or current dose escalation planned Planned pulmonary endarterectomy or pulmonary balloon angioplasty. LVEF < 50% Diagnosis of PAH group 2, 3 or 5