Specific Gravity Calculator with Steps (Free) | StatsUnlock

A specific gravity calculator divides the density of a sample by the density of water at a stated temperature. For ethanol at 0.7893 g/mL against water at 20 °C (0.998207 g/mL), SG = 0.7893 ÷ 0.998207 = 0.7907. With a density known to ±0.0005 g/mL, SG = 0.79072 ± 0.00058 (k = 2).

Rule of thumb: specific gravity has no units, but it always has two temperatures (sample/reference). Against water at 4 °C, SG equals the density in g/mL; against 20 °C or 60 °F water it is about 0.1 to 0.2% higher.

Specific gravity (SG), also called relative density, is the density of a substance divided by the density of a reference: water for liquids and solids, air for gases. Because it is a ratio, it has no units. A specific gravity calculator turns density into SG and back at any reference temperature, measures SG from weighings, and applies the SG formulas used in brewing, construction, petroleum, gas engineering and the clinical lab.

A worked one-liner: SG = ρ ÷ ρ_water = 0.7893 g/mL ÷ 0.998207 g/mL = 0.7907 for ethanol at 20 °C. A US gallon of it weighs 0.7893 × 8.3454 = 6.587 lb, and its API gravity is 141.5 ÷ 0.7907 − 131.5 = 47.5°.

Who uses it: chemistry and physics students; homebrewers, winemakers and mead and cider makers reading hydrometers; civil and geotechnical labs testing aggregate and soil (ASTM C127, C128, D854); fuel handlers converting gallons to pounds; gas engineers; and clinical labs reading urine specific gravity. One page replaces separate density, ABV, Plato, aggregate, soil, gas and urine calculators.

Quick answers to the questions people ask most

4.1 What the result means

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4.2 How sure you can be

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4.3 The physics behind it

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4.4 The detail that changes the answer

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4.5 What to do next

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4.6 SG 20/4, 20/20 and 60/60: which one?

The first number is the sample temperature and the second is the water reference temperature. SG 20/4 (water at 4 °C, its densest, 0.99997 g/mL) is numerically equal to density in g/mL, which is why older chemistry handbooks used it. SG 20/20 and 25/25 are common in laboratories because sample and water are at the same temperature. SG 60/60 °F is the petroleum, brewing and API standard. For ethanol at 0.7893 g/mL, the three references give 0.7893, 0.7901 and 0.7907. Water densities here follow Tanaka et al. (2001).

4.7 Specific gravity, specific weight and specific volume

Specific gravity is a ratio with no units. Specific weight is weight per volume, γ = ρg, in N/m³ water is about 9.79 kN/m³ at 20 °C. Specific volume is volume per mass, 1/ρ, in m³/kg. To get pounds per gallon, multiply the density in g/mL by 8.3454; to get pressure under a column of liquid, P = ρgh, so 10 m of SG 1.18 acid adds about 115.6 kPa (16.8 psi).

4.8 When SG is only an estimate

Mixtures that shrink on mixing, such as ethanol and water (Marsh and Richards, 1980), break simple SG to composition rules, which is why the brewing ABV formulas are approximations. Urine SG is a proxy for osmolality, but protein and glucose distort it, and the two correlate only loosely (Leech and Penney, 1987). Gas SG assumes ideal behavior, which fails at high pressure.

A specific gravity result needs the value, the two temperatures (sample/reference), the reference substance (water or air), the method and, for measured values, the uncertainty. The seven write-ups below are filled from the specific gravity calculator; they show the headline example until you press Calculate.

Showing the headline example (ethanol, 0.7893 g/mL, 20 °C reference). Press Calculate above to fill all seven write-ups with your own result.

5.1 What to include

5.2 Seven ready-to-copy write-ups

The same worked problem as Sections 0, 9, 10, 11 and 14: the specific gravity of ethanol, density 0.7893 g/mL ± 0.0005, against water at 20 °C.

1. Pick what you want to calculate. Choose a mode in Section 2: density and specific gravity, measure by weighing, brewing ABV and Plato, gas specific gravity, or urine specific gravity.
2. Load a sample or start from your numbers. Twelve worked problems are in the sample menu. Sample 1 is the headline problem. Nothing is calculated until you press Calculate.
3. Set the reference temperature. Choose water at 4 °C, 60 °F, 20 °C, 25 °C or your own temperature. Specific gravity always needs it.
4. Enter density or SG with its unit. Type the value in g/mL, kg/m³, lb/gal or lb/ft³, or pick a material to fill a typical density.
5. Or enter your weighings. For pycnometer, Archimedes, aggregate or soil tests, type each mass and the water temperature.
6. Add the tolerances. Give the density, balance or hydrometer tolerance. The page combines them by the GUM rule and reports U at k = 2.
7. Press Calculate Specific Gravity. Press the button or Enter. The answer, a Verified badge, the working, every step and a results table appear in Section 3.
8. Read the figure and charts. The figure is drawn from your numbers; the charts compare common materials, show temperature or pressure effects, the measurements and the uncertainty.
9. Copy the write-up. Section 5 fills seven ready texts for a report, a QC record, a method statement, an exam, chat, a results paragraph and a table.
10. Export or run a batch. Download Doc or PDF, or use the Batch tab to convert many densities or SG values at once, typed or from a CSV or Excel file.

Excel can reproduce this specific gravity calculator with one formula for water density and one division. The sheet repeats the headline problem (ethanol, 0.7893 g/mL, 20 °C reference), so the numbers match Sections 0, 7, 10, 11 and 14.

9.1 The formulas you need

9.2 Step by step

9.3 A brewing log

Put OG in column G and FG in column H for each batch. In I2 type =(G2-H2)*131.25 for ABV and in J2 =(G2-H2)/(G2-1)*100 for apparent attenuation, then fill down.

9.4 Why Excel may differ from R or Python

9.5 Charting

Fill A2:A42 with 0 to 40 and B2:B42 with the water-density formula. A Scatter chart with smooth lines shows water densest at 4 °C and falling by about 0.8% by 40 °C.

9.6 Errors you may see

• #DIV/0!: the water density cell is empty.
• #VALUE!: a unit typed into a number cell.
• SG above 1 for a fuel: density was in kg/m³; divide by 1000 first.

A complete, copy-and-run script that reproduces the specific gravity calculator for the headline problem. It computes the water reference density, SG, lb/gal and API gravity, the uncertainty, a brewing ABV with Plato, an aggregate test and a gas SG, and saves one 300 dpi figure.

10.1 The complete script

R, base only, saves water_density.png

# Specific gravity from density with GUM uncertainty, brewing ABV, aggregate and gas SG
# StatsUnlock - https://statsunlock.com/specific-gravity-calculator/   Base R only.

water_density <- function(t)   # air-free water, g/mL, 0-40 C (Tanaka et al., 2001)
  999.974950 * (1 - (t - 3.983035)^2 * (t + 301.797) / (522528.9 * (t + 69.34881))) / 1000

# ---- 1. Inputs ----
rho <- 0.7893; tol_rho <- 0.0005   # ethanol, g/mL
t_ref <- 20                        # reference water temperature, C

# ---- 2. Specific gravity and other units ----
rho_w <- water_density(t_ref)
sg <- rho / rho_w
cat(sprintf("Water at %g C = %.6f g/mL -> SG = %.5f\n", t_ref, rho_w, sg))
cat(sprintf("%.3f lb/gal (US), %.1f kg/m3, API %.1f deg\n", rho * 8.345404, rho * 1000, 141.5 / sg - 131.5))

# ---- 3. Uncertainty: u = a / sqrt(3), U = 2u ----
u <- sg * (tol_rho / sqrt(3)) / rho
cat(sprintf("SG = %.5f +/- %.5f (k = 2)\n", sg, 2 * u))
stopifnot(abs(sg * rho_w - rho) < 1e-12)

# ---- 4. Brewing ----
og <- 1.050; fg <- 1.010
plato <- function(s) -616.868 + 1111.14 * s - 630.272 * s^2 + 135.997 * s^3
cat(sprintf("ABV = %.2f%% (alternate %.2f%%); OG = %.1f P, FG = %.1f P\n",
            (og - fg) * 131.25, 76.08 * (og - fg) / (1.775 - og) * fg / 0.794, plato(og), plato(fg)))

# ---- 5. Aggregate and gas ----
A <- 2000; B <- 2030; C <- 1250
cat(sprintf("Aggregate: Gsb %.3f, Gsb(SSD) %.3f, Gsa %.3f, absorption %.2f%%\n", A/(B-C), B/(B-C), A/(A-C), 100*(B-A)/A))
cat(sprintf("Methane SG = %.3f (air = 1)\n", 16.043 / 28.9647))

# ---- 6. One 300 dpi figure ----
t <- seq(0, 40, by = 0.5)
png("water_density.png", width = 6, height = 4, units = "in", res = 300)
plot(t, water_density(t), type = "l", lwd = 2.5, col = "#2563eb", xlab = "Temperature (C)", ylab = "Water density (g/mL)")
points(c(4, 15.5556, 20, 25), water_density(c(4, 15.5556, 20, 25)), pch = 19, col = "#9333ea")
invisible(dev.off())

10.2 Output

Water at 20 C = 0.998207 g/mL -> SG = 0.79072
6.587 lb/gal (US), 789.3 kg/m3, API 47.5 deg
SG = 0.79072 +/- 0.00058 (k = 2)
ABV = 5.25% (alternate 5.34%); OG = 12.4 P, FG = 2.6 P
Aggregate: Gsb 2.564, Gsb(SSD) 2.603, Gsa 2.667, absorption 1.50%
Methane SG = 0.554 (air = 1)

10.3 Traps

• In sprintf, write a percent sign as %%.
• round() rounds half to even; format with sprintf.
• The water-density function is vectorized: pass a whole vector of temperatures.

10.4 What each part does

10.5 Adapting it

Change rho and t_ref for your liquid. For brewing, change og and fg; for aggregate, A, B and C. Keep temperatures in °C for the water-density function.

A complete, copy-and-run script that reproduces the specific gravity calculator for the headline problem. It computes the water reference density, SG, lb/gal and API gravity, the uncertainty, a brewing ABV with Plato, an aggregate test and a gas SG, and saves one 300 dpi figure.

Install once: pip install numpy matplotlib

11.1 The complete script

Python with NumPy and Matplotlib, saves water_density.png

# Specific gravity from density with GUM uncertainty, brewing ABV, aggregate, gas SG and one figure
# StatsUnlock - https://statsunlock.com/specific-gravity-calculator/
import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt

def water_density(t):
    """Air-free water density, g/mL, 0-40 C (Tanaka et al., 2001, Metrologia 38, 301)."""
    return 999.974950 * (1 - (t - 3.983035) ** 2 * (t + 301.797) / (522528.9 * (t + 69.34881))) / 1000

# ---- 1. Inputs ----
rho, tol_rho = 0.7893, 0.0005      # ethanol density g/mL and its +/- tolerance
t_ref = 20.0                       # reference water temperature, C

# ---- 2. Specific gravity and other units ----
rho_w = water_density(t_ref)
sg = rho / rho_w
print(f"Water at {t_ref:g} C = {rho_w:.6f} g/mL -> SG = {sg:.5f}")
print(f"{rho * 8.345404:.3f} lb/gal (US), {rho * 1000:.1f} kg/m3, API {141.5 / sg - 131.5:.1f} deg")

# ---- 3. Uncertainty: rectangular tolerance u = a/sqrt(3), U = 2u ----
u = sg * (tol_rho / np.sqrt(3)) / rho
print(f"SG = {sg:.5f} +/- {2 * u:.5f} (k = 2)")
sim = np.random.default_rng(1).uniform(rho - tol_rho, rho + tol_rho, 100_000) / rho_w
print(f"Monte Carlo: SD = {sim.std(ddof=1):.6f}, 95% interval {np.percentile(sim, 2.5):.5f} to {np.percentile(sim, 97.5):.5f}")
assert abs(sg * rho_w - rho) < 1e-12

# ---- 4. Brewing: ABV and Plato ----
og, fg = 1.050, 1.010
abv = (og - fg) * 131.25
alt = 76.08 * (og - fg) / (1.775 - og) * fg / 0.794
plato = lambda s: -616.868 + 1111.14 * s - 630.272 * s**2 + 135.997 * s**3
print(f"ABV = {abv:.2f}% (alternate {alt:.2f}%); OG = {plato(og):.1f} P, FG = {plato(fg):.1f} P")

# ---- 5. Aggregate (A oven-dry, B SSD, C in water) and gas ----
A, B, C = 2000.0, 2030.0, 1250.0
print(f"Aggregate: Gsb {A/(B-C):.3f}, Gsb(SSD) {B/(B-C):.3f}, Gsa {A/(A-C):.3f}, absorption {100*(B-A)/A:.2f}%")
print(f"Methane SG = {16.043 / 28.9647:.3f} (air = 1)")

# ---- 6. One 300 dpi figure: water density vs temperature ----
t = np.linspace(0, 40, 81)
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(t, water_density(t), color="#2563eb", lw=2.5)
for tr in (4, 15.5556, 20, 25):
    ax.plot(tr, water_density(tr), "o", color="#9333ea", ms=7)
ax.set_xlabel("Temperature (C)"); ax.set_ylabel("Water density (g/mL)")
ax.set_title("Reference water density at 4, 15.56, 20 and 25 C")
fig.tight_layout(); fig.savefig("water_density.png", dpi=300)

11.2 Output

Water at 20 C = 0.998207 g/mL -> SG = 0.79072
6.587 lb/gal (US), 789.3 kg/m3, API 47.5 deg
SG = 0.79072 +/- 0.00058 (k = 2)
Monte Carlo: SD = 0.000289, 95% interval 0.79024 to 0.79119
ABV = 5.25% (alternate 5.34%); OG = 12.4 P, FG = 2.6 P
Aggregate: Gsb 2.564, Gsb(SSD) 2.603, Gsa 2.667, absorption 1.50%
Methane SG = 0.554 (air = 1)

11.3 Traps

• numpy.std() defaults to ddof=0; use ddof=1.
• The Monte Carlo SD (0.000289) matches u = U/2 from the GUM formula.
• Temperatures in °F must be converted to °C before calling water_density().

11.4 What each part does

11.5 Adapting it

Change rho and t_ref for your liquid. For brewing, change og and fg; for aggregate, A, B and C. Keep temperatures in °C for the water-density function.

12.1 Density of water (the reference)

Air-free water, formula of Tanaka et al. (2001). Last checked: October 2026.

12.2 Specific gravity of common liquids and solids

Typical values near 20 °C from standard handbooks; fuels and oils vary by batch, so use the supplier figure for weight and balance. Last checked: October 2026.

12.3 Specific gravity, °Plato and potential alcohol

°Plato from the ASBC polynomial; potential ABV by (OG − 1.000) × 131.25. Last checked: October 2026.

12.4 Hydrometer temperature correction (calibrated at 60 °F)

From the cubic water-density correction used by brewing software; above about 100 °F cool the sample instead. Last checked: October 2026.

12.5 Gas specific gravity (air = 1)

Ideal gas, R from CODATA 2018 (Tiesinga et al., 2021); molar masses from IUPAC 2021 atomic weights. Real-gas densities differ by up to about 1% near room conditions. Last checked: October 2026.

12.6 Typical specific gravity of soils and aggregates

Typical ranges from geotechnical texts and Prakash et al. (2012). Last checked: October 2026.

12.7 Urine specific gravity

Osmolality ≈ (SG − 1) × 1000 × 30 to 40; the relation is loose (Leech and Penney, 1987). Not medical advice. Last checked: October 2026.

Eight worked problems that cover what a specific gravity calculator meets: a textbook liquid, aviation fuel, beer, mead, concrete aggregate, soil, gas safety and a clinical urine sample. Each number was checked in Python.

The written method, calculator keys and a short standard operating procedure for the headline problem: the specific gravity of ethanol at 20 °C with a 25 mL pycnometer. School students do this under a teacher's supervision and the school's own risk assessment.

14.1 The written method

1. Reference. Water at 20 °C = 0.998207 g/mL.
2. Weigh. Empty, with water, with ethanol, all at 20 °C.
3. Masses. Water = m_w − m_e; ethanol = m_s − m_e.
4. Divide. SG = ethanol mass ÷ water mass.
5. Density. ρ = SG × 0.998207.
6. Check. Ethanol should give about 0.791 (20/20).

14.2 On a scientific calculator

14.3 The lab SOP

14.4 Practice problems

14.5 Mistakes that lose marks or fail an audit

• Giving SG units such as g/mL.
• Leaving out the reference temperature.
• Not correcting a hydrometer for temperature.
• Using the standard ABV formula for a mead or wine.
• Mixing up bulk, SSD and apparent SG for aggregate.
• Not correcting soil Gs to 20 °C.
• Comparing a gas with water instead of air.

14.6 Pre-Lab and Post-Lab Questions

Most specific gravity errors are about temperature, trapped air and choosing the wrong definition. The specific gravity calculator guards against each one below; for aggregates, testing protocol differences shift results more than arithmetic does (Hall, 2004).

For the highest accuracy, use an oscillating U-tube density meter, correct weighings for air buoyancy, and propagate every input (Kragten, 1994).

Your result

The specific gravity calculator gives SG 0.79072 and density 0.7893 g/mL against water at 20 °C. Divide density by the density of water at the reference temperature, and always state that temperature.

What the specific gravity calculator does for the bench

Specific gravity is one ratio used in many trades, each with its own reference temperature, instruments and formulas. This specific gravity calculator handles density and SG at any reference, weighing methods for liquids, solids, aggregate and soil, brewing ABV and Plato with hydrometer correction, gases against air and clinical urine corrections, and puts an uncertainty on measured values.

Watch out for

• An unstated reference temperature.
• Warm hydrometer samples and CO₂ bubbles.
• Trapped air in soil and solid measurements.
• Using the standard ABV formula for strong brews.
• Treating urine SG as a precise osmolality.

Next steps

For repeated readings, the mean calculator and standard deviation calculator give the average and spread. To make a solution of known strength from a dense reagent, use the percent solution calculator. Whatever you measure, start and finish with the specific gravity calculator.

Use these to prepare solutions from dense reagents and to summarize repeated density measurements.

Peer-reviewed sources behind this specific gravity calculator: water and solution densities, ethanol and water mixing, brewing analysis, aggregate and soil specific gravity, gas constants and atomic weights, urine specific gravity and osmolality, and uncertainty. Standards (ASTM C127, C128, D854, D1298; JCGM 100:2008; ASBC methods) are named where they are used. Every DOI checked October 2026.

1. Adams, L. J. (1983). Evaluation of Ames Multistix-SG for urine specific gravity versus refractometer specific gravity. American Journal of Clinical Pathology, 80(6), 871–873. https://doi.org/10.1093/ajcp/80.6.871
2. Chadha, V., Garg, U., & Alon, U. S. (2001). Measurement of urinary concentration: A critical appraisal of methodologies. Pediatric Nephrology, 16(4), 374–382. https://doi.org/10.1007/s004670000551
3. Gales, P. W., & Schwiesow, M. (1993). Automated beer analyzer method for determination of alcohol content and original gravity of beer: Summary of collaborative study. Journal of AOAC International, 76(4), 918–920. https://doi.org/10.1093/jaoac/76.4.918
4. Hall, K. D. (2004). Using a single test to determine specific gravity and absorption of aggregate blends. Transportation Research Record, 1874(1), 3–10. https://doi.org/10.3141/1874-01
5. Hensey, O. J., & Cooke, R. W. (1983). Estimation of urine specific gravity and osmolality using a simple reagent strip. BMJ, 286(6358), 53. https://doi.org/10.1136/bmj.286.6358.53
6. Kragten, J. (1994). Calculating standard deviations and confidence intervals with a universally applicable spreadsheet technique. Analyst, 119(10), 2161–2165. https://doi.org/10.1039/AN9941902161
7. Leech, S., & Penney, M. D. (1987). Correlation of specific gravity and osmolality of urine in neonates and adults. Archives of Disease in Childhood, 62(7), 671–673. https://doi.org/10.1136/adc.62.7.671
8. Marsh, K. N., & Richards, A. E. (1980). Excess volumes for ethanol + water mixtures at 10-K intervals from 278.15 to 338.15 K. Australian Journal of Chemistry, 33(10), 2121–2132. https://doi.org/10.1071/CH9802121
9. Oppliger, R. A., Magnes, S. A., Popowski, L. A., & Gisolfi, C. V. (2005). Accuracy of urine specific gravity and osmolality as indicators of hydration status. International Journal of Sport Nutrition and Exercise Metabolism, 15(3), 236–251. https://doi.org/10.1123/ijsnem.15.3.236
10. Perrier, E. T., Bottin, J. H., Vecchio, M., & Lemetais, G. (2017). Criterion values for urine-specific gravity and urine color representing adequate water intake in healthy adults. European Journal of Clinical Nutrition, 71(4), 561–563. https://doi.org/10.1038/ejcn.2016.269
11. Prakash, K., Sridharan, A., Thejas, H. K., & Swaroop, H. M. (2012). A simplified approach of determining the specific gravity of soil solids. Geotechnical and Geological Engineering, 30(4), 1063–1067. https://doi.org/10.1007/s10706-012-9521-6
12. Prohaska, T., Irrgeher, J., Benefield, J., Böhlke, J. K., Chesson, L. A., Coplen, T. B., Ding, T., Dunn, P. J. H., Gröning, M., Holden, N. E., Meijer, H. A. J., Moossen, H., Possolo, A., Takahashi, Y., Vogl, J., Walczyk, T., Wang, J., Wieser, M. E., Yoneda, S., Zhu, X.-K., & Meija, J. (2022). Standard atomic weights of the elements 2021 (IUPAC Technical Report). Pure and Applied Chemistry, 94(5), 573–600. https://doi.org/10.1515/pac-2019-0603
13. Rogers, P. S. Z., & Pitzer, K. S. (1982). Volumetric properties of aqueous sodium chloride solutions. Journal of Physical and Chemical Reference Data, 11(1), 15–81. https://doi.org/10.1063/1.555660
14. Shergold, F. A. (1953). The test for the apparent specific gravity and absorption of coarse aggregate. Journal of Applied Chemistry, 3(3), 110–117. https://doi.org/10.1002/jctb.5010030305
15. Siebert, K. J. (1980). Routine use of a programmable calculator for computing alcohol, real extract, original gravity, and calories in beer. Journal of the American Society of Brewing Chemists, 38(1), 27–33. https://doi.org/10.1094/asbcj-38-0027
16. Sommerfield, L. M., McAnulty, S. R., McBride, J. M., Zwetsloot, J. J., Austin, M. D., Mehlhorn, J. D., Calhoun, M. C., Young, J. O., Haines, T. L., & Utter, A. C. (2016). Validity of urine specific gravity when compared with plasma osmolality as a measure of hydration status in male and female NCAA collegiate athletes. Journal of Strength and Conditioning Research, 30(8), 2219–2225. https://doi.org/10.1519/JSC.0000000000001313
17. Tanaka, M., Girard, G., Davis, R., Peuto, A., & Bignell, N. (2001). Recommended table for the density of water between 0 °C and 40 °C based on recent experimental reports. Metrologia, 38(4), 301–309. https://doi.org/10.1088/0026-1394/38/4/3
18. Tiesinga, E., Mohr, P. J., Newell, D. B., & Taylor, B. N. (2021). CODATA recommended values of the fundamental physical constants: 2018. Reviews of Modern Physics, 93(2), 025010. https://doi.org/10.1103/RevModPhys.93.025010
19. Voinescu, G. C., Shoemaker, M., Moore, H., Khanna, R., & Nolph, K. D. (2002). The relationship between urine osmolality and specific gravity. The American Journal of the Medical Sciences, 323(1), 39–42. https://doi.org/10.1097/00000441-200201000-00007
20. Williams, P. R., & Kanarek, K. S. (1982). Urine evaporative loss and effects on specific gravity and osmolality. The Journal of Pediatrics, 100(4), 626–628. https://doi.org/10.1016/s0022-3476(82)80772-5