Flat Lambda CDM Distance Calculator
Calculate cosmological distances and lookback time in an entered flat matter-plus-Lambda expansion model.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Numerically integrate the flat expansion model, with radiation and curvature explicitly set to zero.
E(z)=sqrt(Ωm(1+z)³+1−Ωm); Dc=(c/H0)∫dz/E; DL=(1+z)Dc; DA=Dc/(1+z)
Worked example
At redshift zero all reported distances and lookback time are zero. In the matter-only model Dc=2c/H0(1−1/sqrt(1+z)).
Assumptions and input details
Entered model parameters are illustrative, not a current best-fit cosmology. Flat geometry, constant Lambda and pressureless matter, no radiation, peculiar velocities, lensing or parameter uncertainty. Julian-year seconds define Gyr.
References: Hogg: distance measures in cosmology
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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