The　relationships　among　the　ratio　of　indentation　hardness　HIT　over　reduced　elastic　modulus　Er,　the　ratio　of　elastic　work　We　over　total　work　Wt,　and　the　ratio　of　permanent　depth　hp　over　the　maximum　indentation　displacement　hmax　were　investigated　by　instrumented　indentation　of　25　different　materials　under　Berkovich　indenter　and　various　maximum　indentation　loads.　Proportional　relationships　are　found　among　various　indentation　variables　(e.g.　We　vs.　Wt,　HIT　vs.　Er,　and　hp　vs.　hmax).　Quadratic　polynomial　can　be　used　to　express　the　dependence　of　HIT/Er　on　We/Wt　(or　hp/hmax),　based　on　which　indentation　hardness　and　reduced　elastic　modulus　can　be　determined　by　work-based　(or　displacement-based)　approach　without　requiring　area　function　of　the　indenter.　HIT　and　Er　obtained　by　work-based　and　displacement-based　approaches　are　consistent　with　those　obtained　by　Oliver　and　Pharr’s　method　and　those　reported　in　literature.　Graphical　abstract:　[Figure　not　available:　see　fulltext.]　©　2022,　The　Author(s),　under　exclusive　licence　to　The　Materials　Research　Society.