{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"hemocytometer-count"},"result":{"entity_type":"calculator","id":"hemocytometer-count","calculator_id":"hemocytometer-count","canonical_url":"https://tttkmbb.com/science/hemocytometer-count","name":"Hemocytometer Cell Count Calculator","title":"Hemocytometer Cell Count Calculator – Cells per mL, Viability and Volume for a Target Cell Number","category":"science","category_name":"Biology, Earth & Space","tool_name":"calculate_hemocytometer_cell_count","featured_mcp_tool":false,"description":"Converts a hemocytometer count into cell concentration with cells/mL = (cells counted ÷ large squares counted) × dilution factor × 10⁴, and optionally the total cells in a sample, trypan-blue viability and the volume that contains a target number of cells.","use_when":"You counted cells in the large 1 mm² squares of a Neubauer hemocytometer and need the concentration, the number of cells in your flask or the volume to seed a given number of cells.","do_not_use_when":"You counted in the small central squares or used a different chamber depth (adjust the volume per square), used an automated counter, or need cell growth rates (use cell-doubling-time).","inputs":[{"name":"cells_counted","label":"Cells counted","type":"integer","required":true,"min":0,"max":10000000,"description":"Number of (live, unstained) cells counted in all the squares together.","example":200},{"name":"squares_counted","label":"Large squares counted","type":"integer","required":false,"default":4,"min":1,"max":18,"description":"Number of large 1 mm × 1 mm squares counted (each holds 0.1 µL at the standard 0.1 mm depth); typically the 4 corner squares.","example":4},{"name":"dilution_factor","label":"Dilution factor","type":"number","required":false,"default":1,"min":1,"max":1000000,"description":"Dilution of the sample before loading (2 for a 1:1 mix with trypan blue, 10 for 1:9).","example":2},{"name":"sample_volume_ml","label":"Sample volume","type":"number","unit":"mL","required":false,"max":1000000,"exclusive_min":0,"description":"Volume of the original cell suspension; gives the total cell number.","example":10},{"name":"dead_cells_counted","label":"Dead cells counted","type":"integer","required":false,"min":0,"max":10000000,"description":"Stained (dead) cells counted in the same squares; gives the viability.","example":20},{"name":"target_cells","label":"Target cell number","type":"number","required":false,"max":1000000000000000,"exclusive_min":0,"description":"Number of cells you want to take; gives the suspension volume needed.","example":1000000}],"outputs":[{"name":"cells_per_ml","label":"Cell concentration","type":"number","unit":"cells/mL","decimals":0,"description":"(cells_counted / squares_counted) × dilution_factor × 10⁴."},{"name":"cells_per_ml_text","label":"Concentration (scientific)","type":"string","decimals":4,"description":"The concentration in scientific notation."},{"name":"cells_per_square","label":"Average cells per square","type":"number","decimals":2,"description":"cells_counted / squares_counted."},{"name":"poisson_counting_error_percent","label":"Counting error (Poisson)","type":"number","unit":"%","decimals":2,"description":"Relative standard error of the count, 100 / √cells_counted."},{"name":"total_cells","label":"Total cells in sample","type":"number","decimals":0,"description":"cells_per_ml × sample_volume_ml (when the volume is given)."},{"name":"viability_percent","label":"Viability","type":"number","unit":"%","decimals":2,"description":"100 × live / (live + dead) (when dead_cells_counted is given)."},{"name":"total_cells_per_ml","label":"All cells per mL (live + dead)","type":"number","unit":"cells/mL","decimals":0,"description":"Concentration including dead cells (when dead_cells_counted is given)."},{"name":"volume_for_target_ml","label":"Volume for target cells","type":"number","unit":"mL","decimals":4,"description":"target_cells / cells_per_ml (when target_cells is given)."}],"input_schema":{"type":"object","properties":{"cells_counted":{"description":"Number of (live, unstained) cells counted in all the squares together.","type":"integer","minimum":0,"maximum":10000000,"examples":[200]},"squares_counted":{"description":"Number of large 1 mm × 1 mm squares counted (each holds 0.1 µL at the standard 0.1 mm depth); typically the 4 corner squares.","type":"integer","minimum":1,"maximum":18,"default":4,"examples":[4]},"dilution_factor":{"description":"Dilution of the sample before loading (2 for a 1:1 mix with trypan blue, 10 for 1:9).","type":"number","minimum":1,"maximum":1000000,"default":1,"examples":[2]},"sample_volume_ml":{"description":"Volume of the original cell suspension; gives the total cell number. 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Unit: cells/mL.","type":"number","x-unit":"cells/mL"},"cells_per_ml_text":{"description":"The concentration in scientific notation.","type":"string"},"cells_per_square":{"description":"cells_counted / squares_counted.","type":"number"},"poisson_counting_error_percent":{"description":"Relative standard error of the count, 100 / √cells_counted. Unit: %.","type":"number","x-unit":"%"},"total_cells":{"description":"cells_per_ml × sample_volume_ml (when the volume is given).","type":"number"},"viability_percent":{"description":"100 × live / (live + dead) (when dead_cells_counted is given). Unit: %.","type":"number","x-unit":"%"},"total_cells_per_ml":{"description":"Concentration including dead cells (when dead_cells_counted is given). Unit: cells/mL.","type":"number","x-unit":"cells/mL"},"volume_for_target_ml":{"description":"target_cells / cells_per_ml (when target_cells is given). Unit: mL.","type":"number","x-unit":"mL"}}},"formula":"cells/mL = (cells_counted / squares_counted) × dilution_factor × 10⁴; total = cells/mL × sample_volume_ml; viability % = 100 × live / (live + dead); volume_for_target = target_cells / cells/mL","method":"Standard Neubauer geometry: each large square is 1 mm × 1 mm × 0.1 mm = 0.1 µL, so cells per square × 10⁴ = cells per mL. Counting error follows Poisson statistics (≈ 10 % for 100 cells, 7 % for 200), which is why at least 100 cells should be counted.","sources":[{"name":"Wikipedia – Hemocytometer","url":"https://en.wikipedia.org/wiki/Hemocytometer","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Trypan blue","url":"https://en.wikipedia.org/wiki/Trypan_blue","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"200 cells in 4 squares, 1:1 trypan blue, 10 mL flask","inputs":{"cells_counted":200,"squares_counted":4,"dilution_factor":2,"sample_volume_ml":10,"dead_cells_counted":20,"target_cells":1000000},"expected":{"cells_per_ml":1000000,"cells_per_ml_text":"1.00 × 10^6 cells/mL","cells_per_square":50,"total_cells":10000000,"viability_percent":90.91,"volume_for_target_ml":1,"poisson_counting_error_percent":7.07},"url":"https://tttkmbb.com/api/v1/calculate/hemocytometer-count?cells_counted=200&squares_counted=4&dilution_factor=2&sample_volume_ml=10&dead_cells_counted=20&target_cells=1000000"},{"name":"120 cells in 4 squares, undiluted","inputs":{"cells_counted":120,"squares_counted":4,"dilution_factor":1},"expected":{"cells_per_ml":300000,"cells_per_ml_text":"3.00 × 10^5 cells/mL","cells_per_square":30},"url":"https://tttkmbb.com/api/v1/calculate/hemocytometer-count?cells_counted=120&squares_counted=4&dilution_factor=1"}],"faq":[{"q":"Do I enter live cells only?","a":"Enter the unstained (live) cells as cells_counted and the blue (dead) cells as dead_cells_counted; the main concentration is then viable cells per mL and viability is live / (live + dead)."},{"q":"Which dilution factor for trypan blue?","a":"Mixing equal volumes of cells and 0.4 % trypan blue is a 1:1 dilution, so the factor is 2; 10 µL cells + 90 µL stain is a factor of 10."},{"q":"How many cells should I count?","a":"At least 100 in total (ideally 100–200 per large square set); dilute if squares are overcrowded (> 200 per square) and count more squares if there are fewer than about 20 per square."}],"tags":["hemocytometer","cell count","cells per ml","trypan blue viability","neubauer chamber","cell concentration"],"related":[{"calculator_id":"cell-doubling-time","reason":"Doubling time from two counts taken at different times."},{"calculator_id":"dilution","reason":"Dilute the suspension to a target concentration (C1V1 = C2V2)."},{"calculator_id":"centrifuge-rcf-rpm","reason":"Convert the ×g of the pelleting step to rpm."}],"links":{"html":"https://tttkmbb.com/science/hemocytometer-count","markdown":"https://tttkmbb.com/science/hemocytometer-count.md","json":"https://tttkmbb.com/science/hemocytometer-count.json","api":"https://tttkmbb.com/api/v1/calculate/hemocytometer-count","schema":"https://tttkmbb.com/api/v1/calculators/hemocytometer-count","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:44:26Z"}