conditional sentences

English conditional sentences can be divided into the two broad classes of factual/predictive and hypothetical (counterfactual), depending on the form of the verb in the condition (protasis). The terms "factual" and "counterfactual" broadly correspond to the linguistic modalities called realis and irrealis.

Factual

In these constructions, the condition clause expresses a condition the truth of which is unverified. The verb in the condition clause is in the past tense (with a past tense interpretation) or in the present tense (with a present or future tense interpretation). The result clause can be in the past, present, or future. Generally, conditional sentences of this group are in two groups, the "zero conditional" and the potential or indicative conditional, often called "first conditional" or "conditional 1". This class includes universal statements (both clauses in the present, or both clauses in the past) and predictions.
The "zero" conditional is formed with both clauses in the present tense. This construction is similar across many languages. It is used to express a certainty, a universal statement, a law of science, etc.:

If you heat water to 100 degrees celsius, it boils.

If you don't eat for a long time, you become hungry.

If the sea is stormy, the waves are high.

It is different from true conditionals because the introductory "if" can be replaced by "when" or "whenever" (e.g., "When you heat water..."), which cannot be done for true conditionals.
The potential or indicative conditional, often referred to as the "first conditional" or "conditional 1", is used more generally to express a hypothetical condition that is potentially true, but not yet verified. The conditional clause is in the present or past tense and refers to a state or event in the past. The result can be in the past, present, or future. Some examples with the condition clause in the past tense:

If she took that flight yesterday, she arrived at 10pm.

If she took that flight yesterday, she is somewhere in town today.

If she took that flight yesterday, we'll see her tomorrow.

A condition clause (protasis) in the present tense refers to a future event, a current event which may be true or untrue, or an event which could be verified in the future. The result can be in the past, present, or future:

If it's raining here now, then it was raining on the West Coast this morning.

If it's raining now, then your laundry is getting wet.

If it's raining now, there will be mushrooms to pick next week.

If it rains this afternoon, then yesterday's weather forecast was wrong.

If it rains this afternoon, your garden party is doomed.

If it rains this afternoon, everybody will stay home.

If I become President, I'll lower taxes.

Certain modal auxiliary verbs (mainly will, may, might, and could) are not usually used in the condition clause (protasis) in English:

*If it will rain this afternoon, …

*If it may have rained yesterday, …

There are exceptions, however, in which will is used exactly as in the first example, namely when the action in the if clause takes place after that in the main clause:

(The weather forecast says it's going to rain.) Well, if it will rain, we must take umbrellas.

If aspirins will cure it, I'll [I will] take a couple tonight instead of this horrible medicine.^[1]

Other situations in which will can be used in an if clause include when will is not being used as an auxiliary verb, in other words when it is being used modally to express willingness, persistence, or a wish:

If you'll [you will] just hold the door open for me a moment, I can take this table out to the kitchen.

If you will keep all the windows shut, of course you'll get headaches.

If you will excuse me, I think I will slip into something more comfortable.^[1][2]

In colloquial English, the imperative is sometimes used to form a conditional sentence: e.g. "go eastwards a mile and you'll see it" means "if you go eastwards a mile, you will see it".

Counterfactual

In these constructions, the condition clause expresses a condition that is known to be false, or presented as unlikely. The result clause contains a conditional verb form consisting of would (or could, should, might) plus a main verb in the base form (infinitive without to).
The contrary-to-fact present conditional, often referred to as the "second conditional" or "conditional 2", is used to refer to a current state or event that is known to be false or improbable. The past subjunctive (or in colloquial English, simply the past tense) must be used:

If she were [colloq. was] at work today, she would know how to deal with this client.

If I were [colloq. was] the king, I could have you thrown in the dungeon.

The same structure can be used to refer to a future state or event:

If I won the lottery, I would buy a car.

If he said that to me, I would run away.

In many cases, when referring to future events, the difference between a realis and irrealis conditional is very slight:

(realis) If you leave now, you can still catch your train.

(irrealis) If you left now, you could still catch your train.

The contrary-to-fact past conditional (sometime referred to as the "third" conditional, conditional 3) is used to refer to contrary-to-fact past events. The pluperfect (or past perfect) is used in the condition clause.

If you had called me, I would have come.

If you had done your job properly, we wouldn't be in this mess now.

Some varieties of English regularly use would (often shortened to (I)'d) and would have (often shortened to (I)'d have) in counterfactual condition clauses, but this is often considered non-standard: If you'd leave now, you'd be on time. (conditional 2.) / If you (would)'ve told me, we could've done something about it. (conditional 3.) Such use of would is widespread especially in spoken US English in all sectors of society, but these forms are not usually used in more formal writing. Nevertheless, some reliable sources simply label this usage as acceptable US English and no longer label it as colloquial.^[3][4]
There are exceptions, however, where would is used in British English too in seemingly counterfactual conditions, but these can usually be interpreted as a modal use of would: If you would listen to me once in a while, you might learn something. (conditional 2.) ^[1][2] In cases in which the action in the if clause takes place after that in the main clause, use of would in counterfactual conditions is however considered standard and correct usage in even formal UK and US usage: If it would make Bill happy, I'd [I would] give him the money.^[1]
Should can appear in the condition clause to refer to a future event presented as possible, but unlikely, undesirable, or otherwise "remote": If I should die before I wake, …, If you should ever find yourself in such a situation, …

Logic

The material conditional operator used in logic (i.e.) is sometimes read aloud in the form of a conditional sentence (i.e. "if p, then q"), the intuitive interpretation of conditional statements in natural language does not always correspond to the definition of this mathematical relation. Modelling the meaning of real conditional statements requires the definition of an indicative conditional, and contrary-to-fact statements require a counterfactual conditional operator, formalized in modal logic.

Examples

English

In English, there are three conditional sentence formulas. They are:
The first formula indicates the possible outcome of an event that is likely to occur: If + Present Simple/Present Progressive + Present Simple/Present Progressive/Future Simple/Future Progressive/Imperative
The second formula indicates the possible outcome of an event that is less likely to occur:
If + Present Perfect/Present Perfect Progressive/Preterite/Past Continuous + Conditional Present/Conditional Present Progressive
(In some dialects: If + Imperfect Subjunctive + Conditional Present/Conditional Present Progressive)
The third formula indicates the possible outcome of an event that did not occur, and is therefore a missed opportunity: If + Pluperfect/Pluperfect Progressive + Conditional Perfect/Conditional Perfect Progressive
It is possible to reverse the order of the clauses, however, the protasis must always follow the word "If" (Eg. "If + I miss the bus, + I will be late for school" can be adjusted to: "I will be late for school + if + I miss the bus.)

Latin

Conditional sentences in Latin are traditionally classified into three categories, based on grammatical structure.

• simple conditions (factual or logical implications)
  • present tense [if present indicative then indicative]
  • past tense [if perfect/imperfect indicative then indicative]
• future conditions
  • "future more vivid" [if future indicative then future indicative]
  • "future less vivid" [if present subjunctive then present subjunctive]
• contrafactual conditions
  • "present contrary-to-fact" [if imperfect subjunctive then imperfect subjunctive]
  • "past contrary-to-fact" [if pluperfect subjunctive then pluperfect subjunctive]

French

Si + Présent de l'indicatif + Présent de l'indicatif/Futur simple de l'indicatif/Présent de l'impératif
Si + Imparfait de l'indicatif + Présent du conditionnel
Si + Plus-que-parfait de l'indicatif + Passé du conditionnel

Italian

Italian includes the subjunctive in the second and third formulas, and does not allow the present to mix with the future in the first formula:
Se + Presente dell'indicativo + Presente dell'indicativo
Se + Futuro semplice dell'indicativo + Futuro semplice dell'indicativo

Se + Imperfetto del congiuntivo (subjunctive) + Presente del condizionale (or, more informal, Se + Imperfetto dell'indicativo + Imperfetto dell'indicativo)
Se + Trapassato (Pluperfect) del congiuntivo + Passato del condizionale