Treynor = (portfolio return - risk-free rate) / beta. For a book returning 16% against a 5% risk-free rate with a portfolio beta of 1.3: (16 - 5) / 1.3 = 8.5.
The difference from the sharpe-ratio is what sits in the denominator. Sharpe divides by total volatility and so charges you for all risk, including the diversifiable kind. Treynor charges only for systematic-risk, on the assumption that the rest has been diversified away. That assumption is reasonable for a component of a large portfolio and unreasonable for a concentrated trading account.
Use it when comparing holdings inside a diversified portfolio, not for judging a standalone book. For a trader running six correlated positions, most of the risk is not systematic and Treynor will flatter the result substantially.
Related: beta, sharpe-ratio, systematic-risk, jensens-alpha