Lombardi
$$1RM={MaxReps^{0.1} \cdot MaxWeight)}$$
$$MaxReps={\sqrt[0.1]{\frac{1RM}{MaxWeight}}}$$
$$MaxWeight={\frac{1RM}{MaxReps^{0.1}}}$$
Mayhew
$$1RM={\frac{MaxWeight}{0.522 + 0.419 \cdot e^{-0.055 \cdot MaxReps}}}$$
$$MaxReps=-{\frac{\ln\left({\displaystyle\frac{\displaystyle\frac{MaxWeight}{1RM}-0.522}{0.419}}\right)}{0.055}}$$
$$MaxWeight={1RM \cdot (0.522 + 0.419 \cdot e^{-0.055 \cdot MaxReps})}$$
Berger
$$1RM={\frac{MaxWeight}{1.0261 - 0.00262 \cdot MaxReps}}$$
$$MaxReps=-{\left(\frac{\frac{MaxWeight}{1RM} - 1.0261}{0.00262}\right)}$$
$$MaxWeight={1RM \cdot (1.0261 - 0.00262 \cdot MaxReps)}$$
Brown
$$1RM={(MaxReps \cdot 0.0338 + 0.9849) \cdot MaxWeight}$$
$$MaxReps={\frac{1RM - 0.9849 \cdot MaxWeight}{0.0338 \cdot MaxWeight}}$$
$$MaxWeight={\frac{1RM}{MaxReps \cdot 0.0338 + 0.9849}}$$
Welday
$$1RM={(MaxReps \cdot 0.0333) \cdot MaxWeight + MaxWeight}$$
$$MaxReps={\frac{1RM - MaxWeight}{MaxWeight \cdot 0.0333}}$$
$$MaxWeight={\frac{1RM}{MaxReps \cdot 0.0333 + 1}}$$
Eplay
$$1RM={(1 + 0.0333 \cdot MaxReps) \cdot MaxWeight}$$
$$MaxReps={\frac{1RM - MaxWeight}{MaxWeight \cdot 0.0333}}$$
$$MaxWeight={\frac{1RM}{1 + 0.0333 \cdot MaxReps}}$$
Wathen
$$1RM={\frac{MaxWeight}{0.488 + 0.538 \cdot e^{-0.075 \cdot MaxReps}}}$$
$$MaxReps=-{\frac{\ln\left({\displaystyle\frac{\displaystyle\frac{MaxWeight}{1RM}-0.488}{0.538}}\right)}{0.075}}$$
$$MaxWeight={(0.488 + 0.538 \cdot e^{-0.075 \cdot MaxReps}) \cdot 1RM}$$
Brzycki
$$1RM={\frac{MaxWeight}{1.0278 - 0.0278 \cdot MaxReps}}$$
$$MaxReps=-{\frac{MaxWeight - 1RM \cdot 1.0278}{1RM \cdot 0.0278}}$$
$$MaxWeight={1RM \cdot (1.0278 - 0.0278 \cdot MaxReps)}$$
Landers
$$1RM={\frac{100 \cdot MaxWeight}{101.3 - 2.67123 \cdot MaxReps}}$$
$$MaxReps={\frac{101.3 \cdot 1RM - 100 \cdot MaxWeight}{2.67123 \cdot 1RM}}$$
$$MaxWeight={\frac{1RM \cdot (101.3 - 2.67123 \cdot MaxReps)}{100}}$$
Reinolds
$$1RM={\frac{MaxWeight}{0.5551 \cdot e^{-0.0723 \cdot MaxReps + 0.4847}}}$$
$$MaxReps=-{\frac{\ln\left({\displaystyle\frac{MaxWeight}{0.5551 \cdot 1RM}}\right)-0.4847}{0.0723}}$$
$$MaxWeight={(0.5551 \cdot e^{-0.0723 \cdot MaxReps + 0.4847}) \cdot 1RM}$$
Kemmler
$$1RM={MaxWeight \cdot (0.988 + 0.0104 \cdot MaxReps + 0.0019 \cdot MaxReps^2 - 0.0000584 \cdot MaxReps^3}$$
$$MaxWeight={\frac{1RM}{0.988 + 0.0104 \cdot MaxReps + 0.0019 \cdot MaxReps^2 - 0.0000584 \cdot MaxReps^3}}$$
O'Conner
$$1RM={MaxWeight \cdot (1 + 0.025 \cdot MaxReps)}$$
$$MaxReps={\frac{1RM - MaxWeight}{MaxWeight \cdot 0.025}}$$
$$MaxWeight={\frac{1RM}{1 + 0.025 \cdot MaxReps}}$$
Adams
$$1RM={\frac{MaxWeight}{1 - 0.02 \cdot MaxReps}}$$
$$MaxReps={\frac{1RM - MaxWeight}{0.02 \cdot 1RM}}$$
$$MaxWeight={1RM \cdot (1 - 0.02 \cdot MaxReps)}$$
Cummings and Finn
$$1RM={1.175 \cdot MaxWeight + 0.839 \cdot MaxReps - 4.29787}$$
$$MaxReps={\frac{1RM + 4.29787 - 1.175 \cdot MaxWeight}{0.839}}$$
$$MaxWeight={\frac{1RM + 4.29787 - 0.839 \cdot MaxReps}{1.175}}$$
Tucker
$$1RM={1.139 \cdot MaxWeight + 0.352 \cdot MaxReps + 0.243}$$
$$MaxReps={\frac{1RM - 1.139 \cdot MaxWeight - 0.243}{0.352}}$$
$$MaxWeight={\frac{1RM - 0.352 \cdot MaxReps - 0.243}{1.139}}$$