How this calculator works
Enter redshift z, hubble constant h₀ (km/s/mpc), deceleration parameter q₀. CalcStack applies the displayed formula and reports each intermediate planning value with the units shown.
Formula / method
Second-order low-redshift distance = (c ÷ H₀) × [z − ½(1 + q₀)z²]; lookback time ≈ (978 ÷ H₀) × [z − ½(1 + q₀)z²] Gyr; relativistic Doppler β = ((1+z)²−1) ÷ ((1+z)²+1)
Worked example
At z=1 with H₀=70 km/s/Mpc and q₀=−0.55, the second-order approximation gives about 3,319 Mpc and 10.8 Gyr lookback time.
Assumptions and limitations
Redshift is cosmological, the supplied q₀ represents the expansion history over the interval, and the low-redshift series approximation is suitable.
This is not a full ΛCDM numerical integration. Do not use it for precision cosmology, high-redshift objects, peculiar velocities, gravitational redshift, or scientific publication without an appropriate cosmology model.