Velocity　response　spectrum　(SV)　plays　a　critical　role　in　the　seismic　design　of　structures　equipped　with　velocity-dependent　dampers.　Often,　the　SV　is　approximated　using　the　pseudo-velocity　response　spectrum　(PSV),　because　of　the　lack　of　information　on　the　SV　in　seismic　codes.　As　indicated　in　the　existing　literature,　the　error　of　this　approximation　is　significant　for　short　and　long　periods,　and　therefore,　researchers　have　started　to　develop　PSV　to　SV　conversion　models　for　obtaining　SV　more　accurately.　Recent　studies　discovered　that　the　relationship　between　the　PSV　and　SV　is　affected　not　only　by　structural　parameters,　but　also　by　magnitude,　distance,　and　site　class.　However,　models　for　converting　PSV　to　SV　including　magnitude,　distance,　and　site　class　as　input　parameters　have　not　been　developed.　To　this　end,　a　PSV　to　SV　conversion　model　including　magnitude,　distance,　and　site　class　is　proposed　in　this　study　based　on　a　large　number　of　real　ground　motion　records　(16,660　horizontal　acceleration　time　histories)　selected　from　the　Japan　Strong　Motion　Network.　Furthermore,　since　the　magnitude　and　distance　are　not　specified　in　the　seismic　design,　a　response-spectrum-shape　factor,　s,　is　discussed　to　reflect　the　influences　of　magnitude　and　distance.　Accordingly,　an　SV/PSV　model　incorporating　s　is　established.　The　proposed　models　show　better　accuracy　than　the　existing　models　for　cases　with　different　magnitudes,　distances,　and　site　classes.　©　2024　Taylor　&　Francis　Group,　LLC.