Cosmological Redshift Calculator
Converts between redshift z, recession velocity and distance using a simplified Hubble law.
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Cosmological Redshift
Redshift quantifies how much the wavelength of light from a distant source stretches by the time it reaches us. The defining relation is z = (λ_obs - λ_em) / λ_em, where λ_em is the emitted wavelength and λ_obs the wavelength we observe. Equivalently, 1 + z = a(t₀) / a(t_em), where a(t) is the cosmic scale factor — the redshift directly measures how much the universe has expanded since the light was emitted.
Edwin Hubble's 1929 observations of galaxy redshifts versus distance gave the first evidence that the universe is expanding, leading to the Big Bang model. The cosmic microwave background, emitted at the surface of last scattering, has z ≈ 1100, meaning the universe has expanded by a factor of about 1100 since then.
Applications
Cosmological redshift is the workhorse of observational cosmology: it sets distances to galaxies and quasars, calibrates the Hubble constant H₀, and times the cosmic expansion history. LIGO has detected neutron-star mergers with z near 0.01, where electromagnetic counterparts (kilonovae) let us cross-check the gravitational-wave standard siren with the optical redshift.
FAQ
Is cosmological redshift a Doppler effect? Not exactly — it comes from the stretching of space itself between emission and detection, not from local relative motion through space.
Can z be negative? Yes — that would be a blueshift, common for nearby galaxies whose peculiar motion dominates over the cosmic expansion (Andromeda is approaching us).
What is the highest known redshift? As of the mid-2020s, JWST has confirmed galaxies up to z ≈ 13-14, seen as they were only about 300 million years after the Big Bang.
Related Tools
Redshift z to Recession Velocity
Enter redshift z to get both the non-relativistic v = c·z and the relativistic Doppler speed in km/s, plus the fraction of c. z = 0.01 returns 2998 km/s.
CMB Temperature Radio Approx
Computes approximate spectral intensity of the CMB at a given frequency.
Redshift z → velocity (Doppler)
Compute radial velocity from redshift z (non-rel for z<0.1, relativistic above).
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Calculate the maximum daily allowed noise exposure time, T = 8 ÷ 2^((SPL − 85) ÷ 5), from the sound pressure level SPL (dB(A)). The result, in hours, is the maximum exposure duration before reaching a 100% dose under the Brazilian NR-15 (85 dB(A) limit for 8 h, with a 5 dB dose-doubling rate). Every 5 dB above 85 halves the allowed time: 90 dB(A) allows 4 h, 95 dB(A) only 2 h. It is the basis for dose calculation and the planning of rotation and breaks. Enter the sound pressure level.
Oxygen Requirement (Aeration)
Calculate the oxygen requirement of an aerobic treatment system, O₂ = Q × ΔS ÷ 1000 × f, multiplying the flow (m³/day) by the BOD removed (mg/L) and an oxygen-demand factor (typically 1.0–1.5 kg O₂/kg BOD). The result, in kg O₂/day, sizes blowers and aerators in activated sludge and aerated lagoons, ensuring enough oxygen for the biological oxidation of organic matter. Enter the flow, the BOD removed and the oxygenation factor.
Snow mm to cm Ratio Calculator
Converts rain-equivalent millimeters to centimeters of snow applying the typical regional snow liquid ratio (SLR).
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.