Probability Calculator — Percent, Odds & One-in-N

← Research ReefThe Creative Island · Island 13

What are the chances? Fractions to percentages, percentages to one-in-N, odds made honest.

Favorable outcomes

Total outcomes

Dice quick facts: any single face 1/6 ≈ 16.7% · double sixes 1/36 ≈ 2.8% · coin flip 50% · at least one six in four rolls ≈ 51.8%.

How to use this tool

1. Enter the favorable outcomes and the total outcomes (e.g. 1 and 6 for one die face).
2. Press Calculate probability — get the percentage, fraction, one-in-N and odds.
3. The percentage shortcut converts a known percentage the other way.

Example

One specific face of a die: 1/6 = 16.67% = one in 6. Rolling at least one six in four rolls: 1 − (5/6)&sup4; ≈ 51.8% — slightly better than a coin flip, a result most people guess wrong.

The formula

P = favorable ÷ total  |  odds against = (1−P) : P  |  'at least one' = 1 − (1−p)™

What the result means

Probability is long-run frequency, not destiny: a one-in-six event can happen three times in a row, and the die owes you nothing afterwards. The one-in-N form builds intuition ('one in 6 million' lands harder than '0.0000167%'), and 'at least one' problems hide inside exams, lotteries and quality control everywhere.

Frequently asked questions

Why is 'at least one' calculated with subtraction?

Because the direct cases pile up awkwardly. The complement — the event NOT happening every time — is one multiplication: 1 − (5/6)&sup4; for four dice. This trick unlocks a huge family of problems.

Do independent events even out after a streak?

No — the gambler's fallacy. Past rolls don't change future odds; the die has no memory and owes no debts.

Can probability be over 100%?

Never. If your arithmetic says so, some outcomes were double-counted — the classic P(A)+P(B) error when events overlap.

Is my input stored?

No — the calculation happens in your browser.

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Fish Stocking Calculator — How Many Fish Fit Your Tank

← Research ReefThe Creative Island · Island 13

The eternal question — how many fish? Volume, fish size, and a rule of thumb with its limits stated honestly.

Tank volume (litres, actual water)

Adult size of fish (cm)

Stocking approach Conservative (1 cm fish per 2 L) Standard (1 cm fish per 1 L) Heavy (1 cm per 0.5 L — experts, heavy filtration)

Rule-of-thumb stocking is a starting point, not a law — research your species' adult size, shoaling needs, territory and bioload before buying.

How to use this tool

1. Enter your tank's actual water volume in litres (use the Aquarium Volume Calculator for the honest figure).
2. Enter the fish's adult size in cm — not the size in the shop tank.
3. Choose a stocking approach and press Calculate stocking.

Example

A 56 L tank with 5 cm adult tetras, standard rule: 56 ÷ 5 ≈ 11 fish — a proper shoal. The same tank with 12 cm goldfish: 4 fish by arithmetic, but honestly fewer, because goldfish are messy bioload machines.

The formula

fish count ≈ volume ÷ (adult cm × litres-per-cm factor)

What the result means

The litres-per-fish rule encodes a biological truth: water volume and filtration set how much waste bacteria can convert. It ignores species behavior — territory, shoaling, aggression — which is why the result is a ceiling to think under, not a target to hit. Adult size matters most: the 3 cm shop juvenile that grows to 15 cm turns a stocked tank into an overcrowded one.

Frequently asked questions

Is '1 cm per litre' actually reliable?

It's a useful sanity ceiling for small peaceful community fish, and wrong for big, messy or territorial species. Use it to reject bad ideas ('20 goldfish in 40L'), not to design a biotope.

Should I stock to the maximum?

No — experienced keepers stock 50–70% of the ceiling. Understocked tanks are stable, forgiving and easier to keep beautiful.

Does it work for bettas and other solitary fish?

Volume-wise yes, but solitary/territorial species override the count: one betta regardless of what the arithmetic allows, and territorial cichlids need footroom, not just litres.

Is my aquarium data uploaded?

No — the estimate is computed in your browser.

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• The Main Island — drive the boat, explore the whole world.
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Privacy & data: this tool runs entirely in your browser — nothing you type is uploaded, saved or sent anywhere. · Disclaimer: calculations use standard scientific formulas — for lab, safety or field decisions, always double-check with official protocols. · Privacy Policy · Disclaimer

Aquarium Volume Calculator — Litres & Gallons of Your Tank

← Research ReefThe Creative Island · Island 13

How much water is really in there? Rectangular and cylinder tanks, litres and gallons, honest about the air gap at the top.

Tank shape Rectangular Cylinder

Length (cm)

Width (cm)

Height (cm)

Diameter (cm) — cylinder only

Fill level: 90% (water never reaches the rim)

How to use this tool

1. Choose your tank shape: rectangular or cylinder.
2. Measure in cm: length × width × height (or diameter × height).
3. Set the fill level — water always sits below the rim — and read litres and gallons.

Example

A standard 60 × 30 × 35 cm tank: gross 63 L, at 90% fill ≈ 56.7 L — and with a gravel bed and wood, realistically a ~48 L working volume. That's the number your stocking and dosing decisions should use.

The formula

rectangular: L×W×H ÷ 1000 = litres  |  cylinder: π×(D÷2)²×H ÷ 1000

What the result means

Two mistakes ruin tank math: quoting the gross volume (nobody fills to the rim) and ignoring displacement (gravel, wood and filter media replace water). Dosing medication or fertilizer by the gross figure overdoses a smaller real volume — this calculator nudges you toward the honest number.

Frequently asked questions

Why does the tank shop say 60L but this says 56?

Shops quote gross (or marketing) volume. Real water level, glass thickness and decor take 10–20% away — always dose by actual litres.

How do I account for a sump or canister filter?

Add the filter's water volume (sump water depth × area, or ~2–4 L for a typical canister) to the tank's figure for total system volume.

Does shape affect stocking?

Yes — surface area matters more than litres for gas exchange; a long shallow 60L outperforms a tall narrow 60L. Volume is necessary math, not the whole story.

Is my tank data uploaded?

No — computed locally in your browser.

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Molarity Calculator — Moles, Mass and Solutions

← Research ReefThe Creative Island · Island 13

How many grams make a 1 M solution? Mass ↔ moles ↔ molarity, any direction.

Solve for Mass of solute (g) Molarity (M) Volume (L)

Molar mass (g/mol)

Molarity (mol/L)

Volume (L)

Mass (g)

Common molar masses: NaCl 58.44 · glucose 180.16 · KOH 56.11 · CaCO₃ 100.09 (g/mol).

How to use this tool

1. Choose what to solve for — mass, molarity or volume.
2. Enter the molar mass from the label (or the sum of atomic weights).
3. Fill the two known remaining fields and press Calculate.

Example

0.5 L of 0.1 M NaCl: mass = 0.1 × 0.5 × 58.44 = 2.92 g — weigh 2.92 g, dissolve, top up to exactly 500 mL.

The formula

moles = molarity × volume  |  mass = moles × molar mass

What the result means

Molarity counts particles, not grams — one mole is 6.022 × 10²³ molecules, which is why chemists weigh by molar mass: it makes different substances comparable by the number of molecules, not by the number on the scale.

Frequently asked questions

Where do I find the molar mass?

On every reagent bottle label. Or compute it: sum the atomic weights from the formula (NaCl = 22.99 + 35.45 = 58.44 g/mol).

Why does volume use litres?

Because molarity is defined as moles per litre. Working in mL everywhere is fine — just convert: 250 mL = 0.25 L.

Molarity vs molality?

Molarity is per litre of solution; molality is per kilogram of solvent. Molarity rules the typical bench; molality appears when temperature changes volume.

Is my lab data private?

Yes — the calculation happens in your browser.

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• The Main Island — drive the boat, explore the whole world.
• The 90s Kids Island — where most of us started.

Privacy & data: this tool runs entirely in your browser — nothing you type is uploaded, saved or sent anywhere. · Disclaimer: calculations use standard scientific formulas — for lab, safety or field decisions, always double-check with official protocols. · Privacy Policy · Disclaimer

Dilution Calculator — C1V1 = C2V2 Solver

← Research ReefThe Creative Island · Island 13

The lab's favorite equation — solve C1V1 = C2V2 for whatever you're missing.

Solve for Volume of stock needed (V1) Final volume to prepare (V2) Achieved concentration (C2)

C1 (stock conc.)

V1 (stock volume)

C2 (target conc.)

V2 (final volume)

How to use this tool

1. Choose what to solve for — that field is disabled and the others feed it.
2. Enter the known values — keep units consistent (all mL, or all L; all M or all mg/mL).
3. Press Calculate — the answer includes the practical instruction (how much stock, how much diluent).

Example

10 M stock into 0.5 M, final volume 100 mL: V1 = 100 × 0.5 ÷ 10 = 5 mL stock + 95 mL water — a 1:20 dilution.

The formula

C1 × V1 = C2 × V2 (the amount of solute is identical before and after diluting)

What the result means

Dilution conservs solute: whatever molecules were in the stock are all still there after you add water — spread through a bigger volume, hence a smaller concentration. The dilution factor (C1/C2) tells you the ratio at a glance, which is how bench protocols are usually written ('make 1:20').

Frequently asked questions

Does it matter which units I use?

Only consistency does: V1 and V2 in the same unit, C1 and C2 in the same unit. The equation is pure ratios.

Why does 5 mL stock + 95 mL water, not + 100 mL?

Because the final volume is what counts. 5 mL + 95 mL = 100 mL total; adding 100 mL of water would give 105 mL and a wrong concentration — the classic beginner's error.

Can it handle serial dilutions?

Not in one step — compute each stage separately, chaining the output C2 into the next C1. That's also the honest way to catch pipetting-error accumulation.

Is this lab data uploaded?

No — everything is computed in your browser.

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Privacy & data: this tool runs entirely in your browser — nothing you type is uploaded, saved or sent anywhere. · Disclaimer: calculations use standard scientific formulas — for lab, safety or field decisions, always double-check with official protocols. · Privacy Policy · Disclaimer

Scientific Calculator — Free Online with sin, cos, log

← Research ReefThe Creative Island · Island 13

A proper scientific calculator in your browser — trigonometry, logarithms, powers and pi, all computed locally.

Expression

Functions in radians: sin(1.5708) ≈ 1. Use deg conversions like sin(30×3.14159÷180) for degrees, or type sin(0.5236) for sin(30°).

How to use this tool

1. Type an expression or use the function buttons to insert sin, cos, log and friends.
2. Press = (or Enter). Angles are in radians.
3. Press a function button while your cursor is placed to insert exactly there.

Example

sqrt(2) + ln(2.718281828) → 1.4142 + 1 ≈ 2.4142. For degrees: sin(30°) = sin(0.5236 rad) ≈ 0.5.

The formula

expression evaluated with whitelisted Math functions; radians assumed (multiply degrees by π/180)

What the result means

This is real floating-point math with standard library functions — the same results a handheld calculator gives, including the radian convention for trigonometry. Angles in mathematics and physics default to radians; degrees are a convenience of daily life.

Frequently asked questions

Why radians and not degrees?

Radians are the natural unit of mathematics — derivatives and series only work cleanly in radians. Multiply your degrees by π/180 (or 0.01745) before feeding trig functions.

What is the difference between log and ln?

log is base-10 (log(100) = 2), ln is natural base-e (ln(e) = 1). Chemistry uses both; spreadsheets call them LOG10 and LN.

Can I use it for exams?

Use it to check your work — most exams want the method shown, and this tool deliberately shows you only the answer. Learning happens in the steps.

Is my input recorded?

No — evaluation happens locally in your browser.

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Explore the island world

• Research Reef — the island where this tool lives.
• The Main Island — drive the boat, explore the whole world.
• The 90s Kids Island — where most of us started.

Privacy & data: this tool runs entirely in your browser — nothing you type is uploaded, saved or sent anywhere. · Disclaimer: calculations use standard scientific formulas — for lab, safety or field decisions, always double-check with official protocols. · Privacy Policy · Disclaimer