Kepler's Equation Solver
Solve the elliptical form of Kepler's equation, M = E - e sin E, and convert the result to true anomaly. This first active version covers bound elliptical orbits where e is at least 0 and less than 1.
Anomaly solution
Eccentric anomaly
65.201 deg
1.137976 rad
True anomaly
70.524 deg
1.230871 rad
Radius ratio
0.95806 a
instantaneous radius
Residual
-4.4e-16
4 Newton iterations
Mean, eccentric, and true anomaly
e = 0.100
60.00 deg
65.20 deg
70.52 deg
Mean anomaly
Uniform time angle
Eccentric anomaly
Auxiliary circle angle
True anomaly
Focus-to-spacecraft angle
Open Source and Easy to Use Elsewhere
This tool is open source and the underlying logic is fully transparent. You can inspect the code, understand the calculations, and contribute improvements. If you want to use the tool in your own website, course page, or learning platform, you can also embed it directly and start from a ready-made iframe setup for this exact tool.
Open source: review the implementation and see how the results are produced.
Embeddable: preview this tool, copy the iframe, and use it in your own site or LMS.