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Relativistic Velocity Addition — result sheet
Combine two signed collinear subluminal velocities using the special-relativistic velocity-addition formula.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For collinear signed velocities, beta_out = (beta_v + beta_u) / (1 + beta_v beta_u), and v_out = beta_out c with c = 299792458 m/s.
This calculator combines two signed one-dimensional velocities as fractions of c using the special-relativistic velocity-addition relation. It returns the combined fraction and metres-per-second value while keeping acceleration, multidimensional vectors, and frame construction outside the model.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Frame speed as a fraction of c — c; Finite signed one-dimensional frame speed fraction.; minimum -0.999999; maximum 0.999999
- Object speed as a fraction of c — c; Finite signed one-dimensional object speed fraction in the moving frame.; minimum -0.999999; maximum 0.999999
Worked example
| Input | Value |
|---|---|
| Frame speed as a fraction of c | 0.5 |
| Object speed as a fraction of c | 0.75 |
Combining 0.5c and 0.75c gives about 0.9090909c, or 272538598.18 m/s.
Assumptions and limits
- Both inputs are finite signed velocity fractions between -0.999999 and 0.999999, measured along one common line with an explicit positive direction.
- The velocities describe the standard one-dimensional composition of inertial frames, so the denominator 1 + beta_v beta_u remains positive and the combined speed remains subluminal.
- Acceleration history, transverse components, gravitational effects, simultaneity measurements, and navigation or equipment advice are outside the calculation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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